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澳洲代写｜ECON6021｜Financial Economics金融经济学悉尼大学

Posted on 2023年10月11日2023年10月11日 by statistics-lab

statistics-lab^TM为您悉尼大学（英语：The University of Sydney）Financial Economics金融经济学澳洲代写代考和辅导服务！

课程介绍：

This unit provides students with an understanding of the economic foundations of financial theory and the economic framework upon which that theory is based. Much of the work covered is an application of both microeconomic and macroeconomic theory to the special problems encountered in the study of the financial side of an economy. The relevance of these foundations is illustrated with empirical research using Australian and international data.

澳洲代写｜ECON6021｜Financial Economics金融经济学悉尼大学

Attribute	Detail
Course Code	ECON6021
Course Title	Financial Economics
Academic Unit	Economics
Session	Semester 1, 2023
Attendance Mode	Normal day
Location	Camperdown/Darlington, Sydney
Number of Units	6
Course Coordinators/Examiner	Information not provided in the given text
Pre-Requisites	Information not provided in the given text

Contingent claim economy或有债权经济的问题

Basic Characteristics of Option Prices
The owner of a call option has the right, but not the obligation, to buy a given asset in the future at a pre-agreed price, known as the exercise price, or strike price. Similarly, the owner of a put option has the right, but not the obligation,

to sell a given asset in the future at a preagreed price. For each owner (buyer) of an option, there is an option seller, also referred to as the option writer. If the owner of a call (put) option chooses to exercise, the seller must deliver (receive) the underlying asset or commodity in return for receiving (paying) the pre-agreed exercise price. Since an option always has a non-negative payoff to the owner, this buyer of the option must make an initial payment, called the option’s premium, to the seller of the option. ${ }^{10}$

Options can have different features regarding which future date(s) that exercise can occur. A European option can be exercised only at the maturity of the option contract, while an American option can be exercised at any time prior to the maturity of the contract.

Let us define the following notation, similar to that used to describe a forward contract. Let $S_0$ denote the current date 0 price per share of the underlying asset, and let this asset’s price at the maturity date of the option contract, $\tau$, be denoted as $S_\tau$. We let $X$ be the exercise price of the option and denote the date $t$ price of European call and put options as $c_t$ and $p_t$, respectively. Then based on our description of the payoffs of call and put options, we can write the maturity values of European call and put options as
$$
\begin{aligned}
c_\tau & =\max \left[S_\tau-X, 0\right] \
p_\tau & =\max \left[X-S_\tau, 0\right]
\end{aligned}
$$
Now we recall that the payoffs to the long and short parties of a forward contract are $S_\tau-F_{0 \tau}$ and $F_{0 \tau}-S_\tau$, respectively. If we interpret the pre-agreed forward price, $F_0$, as analogous to an option’s preagreed exercise price, $X$, then we see that a call option’s payoff equals that of the long forward payoff whenever thelong forward payoff is positive, and it equals 0 when the long forward payoff is negative. Similarly, the payoff of the put option equals the short forward payoff when this payoff is positive, and it equals 0 when the short forward payoff is negative. Hence, assuming $X=F_{0 \tau}$, we see that the payoff of a call option weakly dominates that of a long forward position, while the payoff of a put option weakly dominates that of a short forward position. ${ }^{11}$ This is due to the consequence of option payoffs always being nonnegative whereas forward contract payoffs can be of either sign.

期权价格的基本特征
看涨期权的所有者有权利（但没有义务）在未来以预先约定的价格（称为执行价格或执行价格）购买特定资产。同样，看跌期权的所有者有权利，但没有义务，

将来以预先约定的价格出售特定资产。对于每个期权的所有者（买方）来说，都有一个期权卖方，也称为期权卖方。如果看涨（看跌）期权的所有者选择行权，卖方必须交付（接收）标的资产或商品，以换取接收（支付）预先约定的行权价格。由于期权总是给所有者带来非负的回报，因此期权的买方必须向期权的卖方支付一笔初始付款，称为期权费。 ${}^{10}$

关于行使的未来日期，期权可以具有不同的特征。欧式期权只能在期权合约到期时行权，而美式期权则可以在合约到期前的任何时间行权。

让我们定义以下符号，类似于用于描述远期合约的符号。令 $S_0$ 表示标的资产的当前日期 0 每股价格，并令该资产在期权合约到期日的价格 $\tau$ 表示为 $S_\tau$。我们让 $X$ 为期权的执行价格，并将欧式看涨期权和看跌期权的日期 $t$ 价格分别表示为 $c_t$ 和 $p_t$。然后根据我们对看涨期权和看跌期权收益的描述，我们可以将欧式看涨期权和看跌期权的到期价值写为$$
\begin{aligned}
c_\tau & =\max \left[S_\tau-X, 0\right] \
p_\tau & =\max \left[X-S_\tau, 0\right]
\end{aligned}
$$

现在我们回想一下，远期合约多头和空头双方的收益分别为 $S_\tau-F_{0 \tau}$ 和 $F_{0 \tau}-S_\tau$。如果我们将预先商定的远期价格 $F_0$ 解释为类似于期权的预先商定的执行价格 $X$，那么我们会看到，只要长期远期收益为正，看涨期权的收益就等于长期远期收益的收益，并且当长期远期收益为负时，它等于 0。同样，当收益为正时，看跌期权的收益等于空头远期收益，当空头远期收益为负时，它等于0。因此，假设 $X=F_{0 \tau}$，我们看到看涨期权的收益微弱地支配多头远期头寸的收益，而看跌期权的收益微弱地支配空头远期头寸的收益。 ${ }^{11}$ 这是因为期权收益总是非负的，而远期合约收益可以是任一符号。

Risk Allocation Principles风险分配原则定义

Principles for the management of operational risk

Operational risk ${ }^5$ is inherent in all banking products, activities, processes and systems, and the effective management of operational risk has always been a fundamental element of a bank’s risk management programme. As a result, sound operational risk management is a reflection of the effectiveness of the board and senior management in administering its portfolio of products, activities, processes, and systems. The Committee, through the publication of this paper, desires to promote and enhance the effectiveness of operational risk management throughout the banking system.

Risk management generally encompasses the process of identifying risks to the bank, measuring exposures to those risks (where possible), ensuring that an effective capital planning and monitoring programme is in place, monitoring risk exposures and corresponding capital needs on an ongoing basis, taking steps to control or mitigate risk exposures and reporting to senior management and the board on the bank’s risk exposures and capital positions. Internal controls are typically embedded in a bank’s day-to-day business and are designed to ensure, to the extent possible, that bank activities are efficient and effective, information is reliable, timely and complete and the bank is compliant with applicable laws and regulation. In practice, the two notions are in fact closely related and the distinction between both is less important than achieving the objectives of each.

Sound internal governance forms the foundation of an effective operational risk management Framework. Although internal governance issues related to the management of operational risk are not unlike those encountered in the management of credit or market risk operational risk management challenges may differ from those in other risk areas.

The Committee is seeing sound operational risk governance practices adopted in an increasing number of banks. Common industry practice for sound operational risk governance often relies on three lines of defence – (i) business line management, (ii) an independent corporate operational risk management function and (iii) an independent review. ${ }^6$ Depending on the bank’s nature, size and complexity, and the risk profile of a bank’s activities, the degree of formality of how these three lines of defence are implemented will vary. In all cases, however, a bank’s operational risk

操作风险${ }^5$是所有银行产品、活动、流程和系统所固有的，操作风险的有效管理一直是银行风险管理计划的基本要素。因此，健全的操作风险管理反映了董事会和高级管理层在管理其产品、活动、流程和系统组合方面的有效性。委员会希望通过发布本文件，促进和提高整个银行体系操作风险管理的有效性。

风险管理通常包括识别银行面临的风险、衡量这些风险的暴露（如果可能）、确保有效的资本规划和监控计划到位、持续监控风险暴露和相应的资本需求、采取措施的过程控制或减轻风险敞口，并向高级管理层和董事会报告银行的风险敞口和资本状况。内部控制通常嵌入银行的日常业务中，旨在尽可能确保银行活动高效、有效，信息可靠、及时和完整，以及银行遵守适用的法律和法规。在实践中，这两个概念实际上密切相关，两者之间的区别并不重要，重要的是实现各自的目标。

健全的内部治理是有效操作风险管理框架的基础。尽管与操作风险管理相关的内部治理问题与信用或市场风险管理中遇到的问题没有什么不同，操作风险管理挑战可能与其他风险领域的挑战不同。

委员会发现越来越多的银行采用了良好的操作风险治理实践。健全的操作风险治理的常见行业惯例通常依赖于三道防线 – (i) 业务线管理，(ii) 独立的公司操作风险管理职能，以及 (iii) 独立审查。 ${ }^6$ 根据银行的性质、规模和复杂性以及银行活动的风险状况，这三道防线实施的正式程度会有所不同。然而，在所有情况下，银行的操作风险

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

金融工程是使用数学技术来解决金融问题。金融工程使用计算机科学、统计学、经济学和应用数学领域的工具和知识来解决当前的金融问题，以及设计新的和创新的金融产品。

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

术语广义线性模型（GLM）通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归，以及方差分析和方差分析（仅含固定效应）。

有限元方法代写

有限元方法（FEM）是一种流行的方法，用于数值解决工程和数学建模中出现的微分方程。典型的问题领域包括结构分析、传热、流体流动、质量运输和电磁势等传统领域。

有限元是一种通用的数值方法，用于解决两个或三个空间变量的偏微分方程（即一些边界值问题）。为了解决一个问题，有限元将一个大系统细分为更小、更简单的部分，称为有限元。这是通过在空间维度上的特定空间离散化来实现的，它是通过构建对象的网格来实现的：用于求解的数值域，它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统，以模拟整个问题。然后，有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

随机分析代写

随机微积分是数学的一个分支，对随机过程进行操作。它允许为随机过程的积分定义一个关于随机过程的一致的积分理论。这个领域是由日本数学家伊藤清在第二次世界大战期间创建并开始的。

时间序列分析代写

随机过程，是依赖于参数的一组随机变量的全体，参数通常是时间。随机变量是随机现象的数量表现，其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值（如1秒，5分钟，12小时，7天，1年），因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中，往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录，以得到其自身发展的规律。

回归分析代写

多元回归分析渐进（Multiple Regression Analysis Asymptotics）属于计量经济学领域，主要是一种数学上的统计分析方法，可以分析复杂情况下各影响因素的数学关系，在自然科学、社会和经济学等多个领域内应用广泛。

MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习和应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

澳洲代写｜MATH2988｜Number Theory and Cryptography Adv 进阶数论与密码学悉尼大学

Posted on 2023年10月11日2023年10月11日 by statistics-lab

statistics-lab^TM为您悉尼大学（英语：The University of Sydney）Applied Financial Econometrics应用金融计量经济学澳洲代写代考和辅导服务！

课程介绍：

This unit of study is an advanced version of MATH2088, sharing the same lectures but with more advanced topics introduced in the tutorials and computer laboratory sessions.

澳洲代写｜MATH2988｜Number Theory and Cryptography Adv 进阶数论与密码学悉尼大学

Attribute	Detail
Course Code	MATH2988
Course Title	Number Theory and Cryptography Adv
Academic Unit	Mathematics and Statistics Academic Operations
Session	Semester 2, 2023
Attendance Mode	Normal day
Location	Camperdown/Darlington, Sydney
Number of Units	6
Course Coordinators	Information not provided in the given text
Tutors	Information not provided in the given text
Pre-Requisites	This unit of study is an advanced version of MATH2088

Computational complexity计算复杂度的问题

Modeling computation and efficiency
We start with an informal description of computation. Let $f$ be a function that takes a string of bits (i.e., a member of the set ${0,1}^$ ) and outputs, say, either 0 or 1 . Informally speaking, an algorithm for computing $f$ is a set of mechanical rules, such that by following them we can compute $f(x)$ given any input $x \in{0,1}^$. The set of rules being followed is finite (i.e., the same set must work for all infinitely many inputs) though each rule in this set may be applied arbitrarily many times. Each rule must involve one of the following “elementary” operations:

Read a bit of the input.
Read a bit (or possibly a symbol from a slightly larger alphabet, say a digit in the set ${0, \ldots, 9})$ from the “scratch pad” or working space we allow the algorithm to use.
Write a bit/symbol to the scratch pad.
Stop and output either 0 or 1 .
Decide which of the above operations to apply based on the values that were just read.

Finally, the running time is the number of these basic operations performed.
Below, we formalize all of these notions.

建模计算和效率
我们从计算的非正式描述开始。令 $f$ 为一个函数，它接受一串位（即集合 ${0,1}^$ 的成员）并输出（例如 0 或 1 ）。通俗地说，计算 $f$ 的算法是一组机械规则，通过遵循这些规则，我们可以在给定任何输入 $x \in{0,1}^$ 的情况下计算 $f(x)$。所遵循的规则集是有限的（即，同一组必须适用于所有无限多个输入），尽管该组中的每个规则可以任意应用多次。每条规则必须涉及以下“基本”操作之一：

读取一点输入。
从我们允许算法使用的“便笺本”或工作空间中读取一点（或者可能是稍大的字母表中的符号，例如集合 ${0, \ldots, 9}）$ 中的一个数字。
将位/符号写入暂存器。
停止并输出 0 或 1 。
根据刚刚读取的值决定应用上述哪一个操作。

最后，运行时间是执行这些基本操作的次数。
下面，我们将所有这些概念形式化。

Theorem 1.6 (EFFicient Universal Turing Machine)
There exists a $T M \mathcal{U}$ and a representation scheme of TM’s satisfying:

Every string $\alpha \in{0,1}^*$ is a representation of some $T M M_\alpha$.
Every TM $M$ is represented by infinitely many strings $\alpha \in{0,1}^*$.
For every $t \in \mathbb{N}$ and $x, \alpha \in{0,1}^*$, if on input $x$, the machine $M_\alpha$ outputs a string $y$ within at most $t$ steps, then $\mathcal{U}(t, x, \alpha)=y$.
On every triple $\langle t, x, \alpha\rangle$, the machine $\mathcal{U}$ runs for at most $C t \log t$ steps, where $C$ is a constant depending on $M_\alpha$ ‘s alphabet and number of states and tapes but independent of $|\alpha|,|x|,|t|$.

To simulate a single computational step of $M$, the machine $\mathcal{U}$ performs the following actions:

Scan the main work tape (the one containing the contents of $M$ ‘s $k$ tapes), and copy into its scratch tape the $k$ symbols that follow the $\star$ symbol of each tape.
Scan the transition function of $M$ to find out how $M$ behaves on these symbols (what $M$ writes on its tapes, how it changes its state register, and how it moves the head). Then write down this information on the scratch pad.
Scan the main work tape and update it (both symbols written and head locations) according to the scratch pad.
Update the tape containing $M$ ‘s state according to the new state.
Use the same head movement and write instructions of $M$ on the input and output tape.
Decrease the counter by 1 , check if it has reached 0 and if so halt.
Now let’s count how many computational steps $\mathcal{U}$ performs to simulate a single step of $M: \mathcal{U}$ ‘s main tape contains at most $k t$ symbols, and so scanning it takes $O(t)$ steps (as $k$ is a constant depending only on $M$ ). Decreasing the counter takes $O(\log t)$ steps. The transition function, the current state, and the scratch pad only require a constant number of bits to store (where this constant depends on $M$ ‘s alphabet size, and number of tapes and states) and so only require a constant number of operations to read and update. Thus, simulating a single step of $M$ takes $O(t+\log t)=O(t)$ operations, and simulating $M$ for $t$ steps takes $O\left(t^2\right)$ operations.
为了模拟 $M$ 的单个计算步骤，机器 $\mathcal{U}$ 执行以下操作：
扫描主工作磁带（包含 $M$ 的 $k$ 磁带内容的磁带），并将每个磁带 $\star$ 符号后面的 $k$ 符号复制到其暂存磁带中。
扫描 $M$ 的转换函数，找出 $M$ 在这些符号上的行为（$M$ 在其磁带上写入什么，它如何更改其状态寄存器，以及它如何移动磁头）。然后将这些信息写在便签本上。
扫描主要工作磁带并根据暂存器更新它（写入的符号和磁头位置）。
根据新状态更新包含 $M$ 状态的磁带。
使用相同的磁头运动并在输入和输出磁带上写入$M$指令。
将计数器减 1，检查它是否已达到 0，如果是则停止。
现在让我们计算一下 $\mathcal{U}$ 执行多少个计算步骤来模拟 $M 的单个步骤： \mathcal{U}$ 的主磁带最多包含 $k t$ 个符号，因此扫描它需要 $O( t)$ 步骤（因为 $k$ 是仅取决于 $M$ 的常数）。减少计数器需要 $O(\log t)$ 步。转换函数、当前状态和暂存器仅需要恒定数量的位来存储（其中该常数取决于 $M$ 的字母大小以及磁带和状态的数量），因此仅需要恒定数量的读取和更新操作。因此，模拟 $M$ 的单个步骤需要 $O(t+\log t)=O(t)$ 操作，而模拟 $M$ 的 $t$ 个步骤需要 $O\left(t^2\right)$ 操作运营。

Euler–Fermat Theorem欧拉-费马定理定义

Euler’s $\phi$-function
Definition :
Let $\mathrm{m} \geq 1$. The Euler $\phi$-function is the function $\phi$-with domain $\mathrm{N}$, the set of positive integers defined as follows :
$\phi(\mathrm{m})$ equals the number of integers in $\mathrm{Z}{\mathrm{m}}$ that are relatively prime to $\mathrm{m}$, e.g., $\phi(1)=1, \phi(2)=1, \phi(3)=2, \phi(4)=2, \phi(5)=4, \phi(6)=2$ and so on. Thus $\phi$ is not a one-to-one function and in case $\mathrm{p}$ is a prime $$ \phi(p)=p-1 . $$ Definition : The residue class $\overline{\mathrm{r}}$ modulo $\mathrm{m}$ is prime to $\mathrm{m}$ if $(\mathrm{r}, \mathrm{m})=1$. Definition A reduced set of residues modulo $m$ is a set of positive integers $\left{r_1, r_2, \ldots . . r{\phi(m)}\right}$ such that exactly one of them lies in each residue class prime to $\mathrm{m}$. If each $r_{\mathrm{i}}$ satisifies $0 \leq \mathrm{r}{\mathrm{i}}<\mathrm{m}$, we called $\left{r_1, r_2, \ldots . r{\phi(m)}\right}$ the reduced set of least positive residues modulo $m$.

For an example, take $\mathrm{m}=6$. Then ${0,1,2,3,4,5}$ is a complete set of residues modulo 6 and ${1,5}$ is a reduced set of least positive residues modulo 6 . In addition ${6,19$, $20,39,16,17}$ is also a complete set of residues, while ${13,17}$ is a reduced set of residues modulo 6 .

We also denote complete set of residues modulo $\mathrm{m}$ by CRS (Mod $\mathrm{m}$ ) and reduced set of least positive residues modulo $\mathrm{m}$ by RRS $(\bmod \mathrm{m})$
Thus CRS $(\bmod 5)={5,13,27,31,34}$
and $\operatorname{RRS}(\bmod 12)={1,5,7,11}$

澳洲代写｜ECMT6006｜Applied Financial Econometrics应用金融计量经济学悉尼大学

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

澳洲代写｜ECMT6006｜Applied Financial Econometrics应用金融计量经济学悉尼大学

Posted on 2023年10月11日2023年10月11日 by statistics-lab

statistics-lab^TM为您悉尼大学（英语：The University of Sydney）Applied Financial Econometrics应用金融计量经济学澳洲代写代考和辅导服务！

课程介绍：

This unit provides an introduction to some of the widely used econometric models designed for the analysis of financial data, and the procedures used to estimate them. Special emphasis is placed upon empirical work and applied analysis of real market data. The unit deals with topics such as: the statistical nature of financial data; the specification, estimation and testing of assets pricing models; the analysis of high frequency financial data; and the modelling of volatility in financial returns. Throughout the unit, students are encouraged (especially in assignments) to familiarise themselves with financial data and learn how to apply the models to these data.

Attribute	Detail
Course Code	ECMT6006
Course Title	Applied Financial Econometrics
Academic Unit	Economics
Session	Semester 1, 2023
Attendance Mode	Normal day
Location	Camperdown/Darlington, Sydney
Number of Units	6
Course Coordinators	Information not provided in the given text
Tutors	Information not provided in the given text
Pre-Requisites	Information not provided in the given text

Applied Financial Econometrics应用金融计量经济学的问题

Which type of the errors are the worst: Type I or II”?
(a) Type I errors
(b) Type II errors
(c) Both Type I and II: It depends on the context
(d) None
Stochastic specification $(\varepsilon)$ in the model is also known as
(a) Error terms
(b) Noise terms
(c) “disturbance terms” or “residuals terms”
(d) All of the above
Panel data often referred as the
(a) Longitudinal data
(b) Cross-sectional data
(c) Time series data
(d) All of the above
Daily mean excess return series of the stock ” $\mathrm{X}$ ” for five years is an example of
(a) Panel data
(b) Pooled data
(c) Time series data
(d) Cross-sectional data
Which of the following is an example of open source software?
(a) EViews
(b) SPSS(c) SAS(d) R programming
Which among the following is not a logical operator?
(a)! “NOT”
(b) \&\& “AND”
(c) || “OR”
(d) $==$ “Equal”
Descriptive statistics estimates of a variable includes:
(a) Mean
(b) Median
(c) Skewness \& Kurtosis
(d) All of the above
Which among the following is not used for testing the unit root ?
(a) Augmented Dickey-Fuller Test
(b) Phillips-Perron test
(c) KPSS test
(d) BDS independence test
Which among the following test is/are used for correlation analysis?
(a) Kendall’s tau
(b) Spearman’s rank correlation
(c) Pearson correlation
(d) All of the above
Which among the following test is not used for the time series normality test?
(a) Shapiro-Wilk test
(b) Jarque-Bera test
(c) Phillips-Perron test
(d) Anderson-Darling test

Applied Financial Econometrics应用金融计量经济学问题2

A professor ask his/her student to do a basic comparative analysis of the COVID-19 first and second phase impact on the Asian stock markets ? Assume yourself as the student and perform the task. Then prepare a detailed report of the analysis to be submitted to the professor.
A researcher want to conduct elementary analyse on the performance of cryptocurrencies during the noble Coronavirus pandemic. Assume yourself as the researcher: perform the mentioned task in details and develop the analysis report.
42 M. MAITI
A Financial analyst want to study the elementary performances of the world indices before, during, and after the first phase of COVID19. Help him/her to perform the said analysis and prepare the report.
A student need to perform descriptive examination on the major three currency pairs exchange rate for the last three years as his/her project dissertation. Help the student to complete his/her project dissertation successfully and satisfactorily.
A senior manager of the Reserve bank of India (RBI) asked an intern working under him/her to prepare a detailed report on the total amount of paperless transactions done in India through the various medium before and during the COVID-19 first phase. Help the intern in analysing and developing the final report for timely submission to the senior RBI manager.

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

澳洲代写｜MATH3979｜Complex Analysis (Advanced)进阶复杂分析悉尼大学

Posted on 2023年10月10日2023年10月10日 by statistics-lab

statistics-lab^TM为您悉尼大学（英语：The University of Sydney）Financial Derivatives 金融衍生工具澳洲代写代考和辅导服务！

课程介绍：

This unit continues the study of functions of a complex variable introduced in the second year unit Analysis (MATH2023/2923). It is aimed at highlighting certain topics from analytic function theory that have wide applications and intrinsic beauty. By learning about the analysis of functions of a complex variable, you will acquire a very important background for mathematical areas such as dynamics, algebraic and differential geometry, and number theory; and advanced theoretical physics such as quantum mechanics, string theory, and quantum field theory. The unit will begin with a revision of properties of complex numbers and complex functions. This will be followed by material on conformal mappings, Riemann surfaces, complex integration, entire and analytic functions, the Riemann mapping theorem, analytic continuation, and Gamma and Zeta functions. Finally, special topics chosen by the lecturer will be presented, which may include elliptic functions, normal families, Julia sets, functions of several complex variables, or complex manifolds. At the end of this unit you will have received a broad introduction and gained a variety of tools to apply them within your further mathematical studies and/or in other disciplines.

澳洲代写｜MATH3979｜Complex Analysis (Advanced)进阶复杂分析悉尼大学

Attribute	Detail
Course Code	MATH3075
Course Title	Financial Derivatives
Coordinating Unit	Mathematics and Statistics Academic Operations
Semester	Semester 2, 2023
Mode	Normal day
Delivery Location	Camperdown/Darlington, Sydney
Number of Units	6
Pre-Requisites	ECB1101, ECC1000, ECF1100, ECS1101, ECW1101
Lecturers	Associate Professor Paola Labrecciosa

Complex Analysis (Advanced)进阶复杂分析的基础理论

I, §1. DEFINITION
The complex numbers are a set of objects which can be added and multiplied, the sum and product of two complex numbers being also a complex number, and satisfy the following conditions.

Every real number is a complex number, and if $\alpha, \beta$ are real numbers, then their sum and product as complex numbers are the same as their sum and product as real numbers.
There is a complex number denoted by $i$ such that $i^2=-1$.
Every complex number can be written uniquely in the form $a+b i$ where $a, b$ are real numbers.
The ordinary laws of arithmetic concerning addition and multiplication are satisfied. We list these laws:
If $\alpha, \beta, \gamma$ are complex numbers, then $(\alpha \beta) \gamma=\alpha(\beta \gamma)$, and
$$
(\alpha+\beta)+\gamma=\alpha+(\beta+\gamma) .
$$

我们有$alpha(\beta+\gamma)=\alpha \beta+\alpha \gamma$，并且$(\beta+\gamma) \alpha=\beta \alpha+\gamma \alpha$。
我们有$\alpha \beta=\beta\alpha$，并且$\alpha+\beta=\beta+\alpha$。
如果1是实数1，那么$1 \alpha=\alpha$。
如果 0 是实数零，那么 $0 \alpha=0$。
我们有 $\alpha+(-1) \alpha=0$。
现在我们将得出这些性质的结果。对于每个复数 $a+b i$，我们关联平面上的点 $(a，b)$。让 $\alpha=a_1+a_2 i$ 和 $\beta=b_1+b_2 i$ 是两个复数。那么
$$
\α+\beta=a_1+b_1+\left(a_2+b_2\right) i .
$$
因此，复数的加法是 “按分量 “进行的。例如，$(2+3 i)+(-1+5 i)=1+8 i$.

Complex Analysis (Advanced)进阶复杂分析的定义相关

The absolute value of a complex number satisfies the following properties. If $\alpha, \beta$ are complex numbers, then
$$
\begin{gathered}
|\alpha \beta|=|\alpha||\beta|, \
|\alpha+\beta| \leqq|\alpha|+|\beta| .
\end{gathered}
$$
Proof. We have
$$
|\alpha \beta|^2=\alpha \beta \overline{\alpha \beta}=\alpha \bar{\alpha} \beta \bar{\beta}=|\alpha|^2|\beta|^2 .
$$

Taking the square root, we conclude that $|\alpha||\beta|=|\alpha \beta|$, thus proving the first assertion. As for the second, we have
$$
\begin{aligned}
|\alpha+\beta|^2=(\alpha+\beta)(\overline{\alpha+\beta}) & =(\alpha+\beta)(\bar{\alpha}+\bar{\beta}) \
& =\alpha \bar{\alpha}+\beta \bar{\alpha}+\alpha \bar{\beta}+\beta \bar{\beta} \
& =|\alpha|^2+2 \operatorname{Re}(\beta \bar{\alpha})+|\beta|^2
\end{aligned}
$$
because $\alpha \bar{\beta}=\overline{\beta \bar{\alpha}}$. However, we have
$$
2 \operatorname{Re}(\beta \bar{\alpha}) \leqq 2|\beta \bar{\alpha}|
$$
because the real part of a complex number is $\leqq$ its absolute value. Hence
$$
\begin{aligned}
|\alpha+\beta|^2 & \leqq|\alpha|^2+2|\beta \bar{\alpha}|+|\beta|^2 \
& \leqq|\alpha|^2+2|\beta||\alpha|+|\beta|^2 \
& =(|\alpha|+|\beta|)^2 .
\end{aligned}
$$
Taking the square root yields the second assertion of the theorem.
The inequality
$$
|\alpha+\beta| \leqq|\alpha|+|\beta|
$$
is called the triangle inequality. It also applies to a sum of several terms. If $z_1, \ldots, z_n$ are complex numbers then we have
$$
\left|z_1+\cdots+z_n\right| \leqq\left|z_1\right|+\cdots+\left|z_n\right| .
$$
Also observe that for any complex number $z$, we have
$$
|-z|=|z|
$$

Theorem 2.1 justifies our notation, by showing that the exponential of complex numbers satisfies the same formal rule as the exponential of real numbers.
Let $\alpha=a_1+i a_2$ be a complex number. We define $e^\alpha$ to be
$$
e^{a_1} e^{i a_2}
$$
For instance, let $\alpha=2+3 i$. Then $e^\alpha=e^2 e^{3 i}$.
Theorem 2.2. Let $\alpha, \beta$ be complex numbers. Then
$$
e^{\alpha+\beta}=e^\alpha e^\beta .
$$
Proof. Let $\alpha=a_1+i a_2$ and $\beta=b_1+i b_2$. Then
$$
\begin{aligned}
e^{\alpha+\beta} & =e^{\left(a_1+b_1\right)+i\left(a_2+b_2\right)}=e^{a_1+b_1} e^{i\left(a_2+b_2\right)} \
& =e^{a_1} e^{b_1} e^{i a_2+i b_2} .
\end{aligned}
$$
Using Theorem 2.1, we see that this last expression is equal to
$$
e^{a_1} e^{b_1} e^{i a_2} e^{i b_2}=e^{a_1} e^{i a_2} e^{b_1} e^{i b_2}
$$
By definition, this is equal to $e^\alpha e^\beta$, thereby proving our theorem.
Theorem 2.2 is very useful in dealing with complex numbers. We shall now consider several examples to illustrate it.
Example 1. Find a complex number whose square is $4 e^{i \pi / 2}$.
Let $z=2 e^{i \pi / 4}$. Using the rule for exponentials, we see that $z^2=4 e^{i \pi / 2}$.
Example 2. Let $n$ be a positive integer. Find a complex number $w$ such that $w^n=e^{i \pi / 2}$.

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

澳洲代写｜MATH3075｜Financial Derivatives 金融衍生工具悉尼大学

Posted on 2023年10月10日2023年10月10日 by statistics-lab

statistics-lab^TM为您悉尼大学（英语：The University of Sydney）Financial Derivatives 金融衍生工具澳洲代写代考和辅导服务！

课程介绍：

This unit will introduce you to the mathematical theory of modern finance with the special emphasis on the valuation and hedging of financial derivatives, such as: forward contracts and options of European and American style. You will learn about the concept of arbitrage and how to model risk-free and risky securities. Topics covered by this unit include: notions of a martingale and a martingale measure, the fundamental theorems of asset pricing, complete and incomplete markets, the binomial options pricing model, discrete random walks and the Brownian motion, the Black-Scholes options pricing model and the valuation and hedging of exotic options. Students completing this unit have been highly sought by the finance industry, which continues to need graduates with quantitative skills. Lectures in the mainstream unit are held concurrently with those of the corresponding advanced unit.

澳洲代写｜MATH3075｜Financial Derivatives 金融衍生工具悉尼大学

Attribute	Detail
Course Code	MATH3075
Course Title	Financial Derivatives
Coordinating Unit	Mathematics and Statistics Academic Operations
Semester	Semester 2, 2023
Mode	Normal day
Delivery Location	Camperdown/Darlington, Sydney
Number of Units	6
Pre-Requisites	ECB1101, ECC1000, ECF1100, ECS1101, ECW1101
Lecturers	Associate Professor Paola Labrecciosa

Financial Derivatives 金融衍生工具的基础理论

“Derivative” includes

Security derived from a debt instrument, share, loan whether secured or unsecured, risk instrument or contract for differences or any other form of security.
A contract which derives its value from the prices, or index of prices of underlying securities.
The above definition conveys that
The derivatives are financial products.
Derivative is derived from another financial instrument/contract called the underlying. In the case of Nifty futures, Nifty index is the underlying. A derivative derives its value from the underlying assets. Accounting Standard SFAS133 defines a derivative as, ‘a derivative instrument is a financial derivative or other contract with all three of the following characteristics:
(i) It has (1) one or more underlings, and (2) one or more notional amount or payments provisions or both. Those terms determine the amount of the settlement or settlements.
(ii) It requires no initial net investment or an initial net investment that is smaller than would be required for other types of contract that would be expected to have a similar response to changes in market factors.
(iii) Its terms require or permit net settlement. It can be readily settled net by a means outside the contract or it provides for delivery of an asset that puts the recipients in a position not substantially different from net settlement

In general, from the aforementioned, derivatives refer to securities or to contracts that derive from another-whose value depends on another contract or assets. As such the financial derivatives are financial instruments whose prices or values are derived from the prices of other underlying financial instruments or financial assets. The underlying instruments may be a equity share, stock, bond, debenture, treasury bill, foreign currency or even another derivative asset. For example, a stock option’s value depends upon the value of a stock on which the option is written. Similarly, the value of a treasury bill of futures contracts or foreign currency forward contract will depend upon the price or value of the underlying assets, such as Treasury bill or foreign currency. In other words, the price of the derivative is not arbitrary rather it is linked or affected to the price of the underlying asset that will automatically affect the price of the financial derivative. Due to this reason, transactions in derivative markets are used to offset thein the underlying assets. In fact, the derivatives can be formed on almost any variable, for example, from the price of hogs to the amount of snow falling at a certain ski resort. risk of price changesin the underlying assets. In fact, the derivatives can be formed on almost any variable, for example, from the price of hogs to the amount of snow falling at a certain ski resort.

“衍生产品 “包括

由债务工具、股票、有担保或无担保贷款、风险工具或差价合约或任何其他形式的证券衍生而来的证券。

从基础证券的价格或价格指数中获取价值的合约。
上述定义表明

衍生产品是金融产品。

衍生产品来源于另一种称为标的物的金融工具/合约。就 Nifty 期货而言，Nifty 指数就是标的物。衍生产品的价值来源于标的资产。会计准则 SFAS133 对衍生工具的定义是：”衍生工具是一种金融衍生工具或具有以下三个特征的其他合同：
(i) 它有：(1) 一个或多个标的；(2) 一个或多个名义金额或支付条款，或两者兼而有之。这些条款决定结算的金额。
(ii) 不需要初始净投资，或初始净投资少于对市场因素变化有类似反应的其他类型的合同。
(iii) 其条款要求或允许净额结算。它可以很容易地通过合同以外的方式进行净结算，或者它规定了一种资产的交割，使接受者处于与净结算没有本质区别的地位。

一般来说，从上述情况来看，衍生工具指的是证券或衍生于另一种合同的合同，其价值取决于另一种合同或资产。因此，金融衍生品是其价格或价值源自其他基础金融工具或金融资产价格的金融工具。基础工具可以是股票、股票、债券、债权、国库券、外币，甚至是另一种衍生资产。例如，股票期权的价值取决于作为期权标的的股票的价值。同样，期货合约的国库券或外币远期合约的价值取决于相关资产（如国库券或外币）的价格或价值。换句话说，衍生产品的价格不是随意确定的，而是与相关资产的价格相关联或受其影响，而相关资产的价格会自动影响金融衍生产品的价格。正因为如此，衍生品市场的交易被用来抵消基础资产的价格。事实上，衍生产品几乎可以针对任何变量，例如，从生猪价格到某个滑雪胜地的降雪量。事实上，衍生工具几乎可以根据任何变量形成，例如，从生猪价格到某个滑雪胜地的降雪量。

Fundamental theorem of asset pricing资产定价基本定理定义相关

The previously constructed “maximal” sequence of semi-martingales $X^n \in \mathcal{X}^1$ converges in a pathwise uniform way in probability, i.e. $\left|X^n-X\right|_1^* \rightarrow 0$ in probability for some càdlàg process $X$.
It is now the goal to show that indeed $X^n \rightarrow X$ in the Emery topology, an apparently much stronger statement. Convergence in the Emery topology can be shown with respect to any equivalent measure $Q \sim P$. since this notion of convergence only depends on the equivalence class of probability measures.
By the basic convergence result (1) we know that $\xi:=\sup _n\left|X^n\right|_1^* \in L^0$. We can therefore find a measure $Q \sim P$ (take, e.g., $d Q / d P=c \exp (-\xi)$ ) such that $X^n \in L^2(Q)$, hence we can continue the analysis with $L^2$-methods, in order to prove Emery-convergence with respect to $Q$. Now the proof starts!
$42 / 24$
先前构建的半马尔廷态 $X^n \ in \mathcal{X}^1$ 的 “最大 “序列在概率上以路径均匀的方式收敛，即对于某个 càdlàg 过程 $X$ ，$\left|X^n-X\right|_1^* \rightarrow 0$ 在概率上收敛。
现在，我们的目标是证明在埃默里拓扑中，$X^n \rightarrow X$ 确实是一个明显更强的陈述。埃默里拓扑中的收敛可以用任何等价度量 $Q \sim P$ 来证明，因为这个收敛的概念只取决于概率度量的等价类。
根据基本收敛结果（1），我们知道 $\xi:=\sup _n\left|X^n\right|_1^* \in L^0$。因此，我们可以找到一个度量 $Q \sim P$（例如，取 $d Q / d P=c \exp (-\xi)$ ），使得 $X^n \ in L^2(Q)$，因此我们可以继续用 $L^2$ 方法进行分析，以证明关于 $Q$ 的埃默里收敛性。现在开始证明
$42 / 24$

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

澳洲代写｜STAT3023｜Statistical Inference统计推断悉尼大学

Posted on 2023年10月10日2023年10月10日 by statistics-lab

statistics-lab^TM为您悉尼大学（英语：The University of Sydney）Statistical Inference统计推断澳洲代写代考和辅导服务！

课程介绍：

In today’s data-rich world more and more people from diverse fields are needing to perform statistical analyses and indeed more and more tools for doing so are becoming available; it is relatively easy to point and click and obtain some statistical analysis of your data. But how do you know if any particular analysis is indeed appropriate? Is there another procedure or workflow which would be more suitable? Is there such a thing as the best possible approach in a given situation? All of these questions (and more) are addressed in this unit. You will study the foundational core of modern statistical inference, including classical and cutting-edge theory and methods of mathematical statistics with a particular focus on various notions of optimality. The first part of the unit covers various aspects of distribution theory which are necessary for the second part which deals with optimal procedures in estimation and testing. The framework of statistical decision theory is used to unify many of the concepts. You will apply the methods learnt to real-world problems in laboratory sessions. By completing this unit you will develop the necessary skills to confidently choose the best statistical analysis to use in many situations.

澳洲代写｜STAT3023｜Statistical Inference统计推断悉尼大学

Attribute	Detail
Course Code	STAT3023
Course Title	Statistical Inference
Coordinating Unit	Mathematics and Statistics Academic Operations
Semester	Semester 2, 2023
Mode	Normal day
Delivery Location	Camperdown/Darlington, Sydney
Number of Units	6
Pre-Requisites	Not provided in the text
Lecturers	Associate Professor Paola Labrecciosa

Statistical Inference统计推断案例

问题 1.

Let $X$ be $P(\lambda)$; that is,
$$
f(x)=e^{-\lambda} \frac{\lambda^x}{x !}, \quad x=0,1,2, \ldots, \quad \lambda>0 .
$$
Then, if $\lambda$ is not an integer, $f(x)$ has a unique mode at $x=[\lambda]$. If $\lambda$ is an integer, then $f(x)$ has two modes obtained for $x=\lambda$ and $x=\lambda-1$.

PROOF For $x \geq 1$, we have
$$
\frac{f(x)}{f(x-1)}=\frac{e^{-\lambda} \lambda^x / x !}{e^{-\lambda} \lambda^{x-1} /(x-1) !}=\frac{\lambda}{x} .
$$
Hence $f(x)>f(x-1)$ if and only if $\lambda>x$, and $f(x)=f(x-1)$ if and only if $x=\lambda$ in case $\lambda$ is an integer. Thus, if $\lambda$ is not an integer, $f(x)$ keeps increasing for $x \leq[\lambda]$ and then decreases. Thus the maximum of $f(x)$ occurs at $x=$ [ $\lambda$ ]. If $\bar{\lambda}$ is an integer, then the maximum occurs at $x=\lambda$. But in this case $f(x)=f(x-1)$, which implies that $x=\lambda-1$ is a second point which gives the maximum value to the p.d.f.

问题 2.

(i) Consider the r.v.’s $X$ and $Y$ with $E X=E Y=0$ and $\operatorname{Var}(X)=$ $\operatorname{Var}(Y)=1$. Then always $-1 \leq E(X Y) \leq 1$, and $E(X Y)=1$ if and only if $P(X=Y)=1$, and $E(X Y)=-1$ if and only if $P(X=-Y)=1$.
(ii) For any r.v.’s $X$ and $Y$ with finite expectations and positive variances $\sigma_X^2$ and $\sigma_Y^2$, it always holds:
$$
-\sigma_X \sigma_Y \leq \operatorname{Cov}(X, Y) \leq \sigma_X \sigma_Y,
$$
and $\operatorname{Cov}(X, Y)=\sigma_X \sigma_Y$ if and only if $P\left[Y=E Y+\frac{\sigma_Y}{\sigma_X}(X-E X)\right]=1$, $\operatorname{Cov}(X, Y)=-\sigma_X \sigma_Y$ if and only if $P\left[Y=E Y-\frac{\sigma_Y}{\sigma_X}(X-E X)\right]=1$.

(i) Clearly, $0 \leq E(X-Y)^2=E X^2+E Y^2-2 E(X Y)=2-2 E(X Y)$, so that $E(X Y) \leq 1$; also, $0 \leq E(X+Y)^2=E X^2+E Y^2+2 E(X Y)=2+2 E(X Y)$, so that $-1 \leq E(X Y)$. Combining these results, we obtain $-1 \leq E(X Y) \leq 1$. As for equalities, observe that, if $P(X=Y)=1$, then $E(X Y)=E X^2=1$, and if $P(X=-Y)=1$, then $E(X Y)=-E X^2=-1$. Next, $E(X Y)=1$ implies $E(X-Y)^2=0$ or $\operatorname{Var}(X-Y)=0$. But then $P(X-Y=0)=1$ or $P(X=Y)=1$ (see Exercise 2.4 in Chapter 3). Also, $E(X Y)=-1$ implies $E(X+Y)^2=0$ or $\operatorname{Var}(X+Y)=0$, so that $P(X=-Y)=1$ (by the exercise just cited).
(ii) Replace the r.v.’s $X$ and $Y$ by the r.v.’s $X^=\frac{X-E X}{\sigma_X}$ and $Y^=\frac{Y-E Y}{\sigma_Y}$, for which $E X^=E Y^=0$ and $\operatorname{Var}\left(X^\right)=\operatorname{Var}\left(Y^\right)={ }^{\sigma_X}$. Then the inequalities $-1 \leq E\left(X^* Y^\right) \leq 1$ become $$ -1 \leq E\left[\left(\frac{X-E X}{\sigma_X}\right)\left(\frac{Y-E Y}{\sigma_Y}\right)\right] \leq 1 $$ from which (31) follows. Also, $E\left(X^ Y^\right)=1$ if and only if $P\left(X^=Y^\right)=$ 1 becomes $E[(X-E X)(Y-E Y)]=\sigma_X \sigma_Y$ if and only if $P\left[Y=E Y+\frac{\sigma_Y}{\sigma_X}\right.$ $(X-E X)]=1$, and $E\left(X^ Y^\right)=-1$ if and only if $P\left(X^=-Y^*\right)=1$ becomes $E[(X-E X)(Y-E Y)]=-\sigma_X \sigma_Y$ if and only if $P\left[Y=E Y-\frac{\sigma_Y}{\sigma_X}(X-E X)\right]=1$. A restatement of the last two conclusions is: $\operatorname{Cov}(X, Y)=\sigma_X \sigma_Y$ if and only if $P\left[Y=E Y+\frac{\sigma_Y}{\sigma_X}(X-E X)\right]=1$, and $\operatorname{Cov}(X, Y)=-\sigma_X \sigma_Y$ if and only if $P\left[Y=E Y-\frac{\sigma_Y}{\sigma_X}\left(\stackrel{\sigma_X}{X}-E X\right)\right]=1$.

问题 3.

COROLLARY 1 If the r.v.’s $X_1, \ldots, X_k$ are independent and distributed as $N\left(\mu, \sigma^2\right)$, then their sample mean $\bar{X} \sim N\left(\mu, \frac{\sigma^2}{k}\right)$, and $\frac{\sqrt{k}(\bar{X}-\mu)}{\sigma} \sim N(0,1)$.

PROOF Here $\bar{X}=Y_1+\cdots+Y_k$, where $Y_i=\frac{X_i}{k}, i=1, \ldots, k$ are independent and $Y_i \sim N\left(\frac{\mu}{k}, \frac{\sigma^2}{k^2}\right)$ by Theorem 2 in Chapter 3 , applied with $c=1 / k$ and $d=0$. Then the conclusion follows by Theorem 4 . The second conclusion is immediate by the part just established and Proposition 1 in Chapter 3, since $\frac{\sqrt{k}(\bar{X}-\mu)}{\sigma}=\frac{\bar{X}-\mu}{\sqrt{\sigma^2 / k}}$.

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

澳洲代写｜OLET5610｜Multivariate Data Analysis多元数据分析悉尼大学

Posted on 2023年10月9日2023年10月9日 by statistics-lab

statistics-lab^TM为您悉尼大学（英语：The University of Sydney）Multivariate Data Analysis多元数据分析澳洲代写代考和辅导服务！

课程介绍：

Machine learning is the process of automatically building mathematical models that explain and generalise datasets. It integrates elements of statistics and algorithm development into the same discipline. Data mining is a discipline within knowledge discovery that seeks to facilitate the exploration and analysis of large quantities for data, by automatic and semiautomatic means. This subject provides a practical and technical introduction to machine learning and data mining. Topics to be covered include problems of discovering patterns in the data, classification, regression, feature extraction and data visualisation. Also covered are analysis, comparison and usage of various types of machine learning techniques and statistical techniques.

澳洲代写｜OLET5610｜Multivariate Data Analysis多元数据分析悉尼大学

Attribute	Detail
Course Code	OLET5610
Course Title	Multivariate Data Analysis
Coordinating Unit	Life and Environmental Sciences Academic Operations
Semester	Intensive June, 2023
Mode	Online
Level	Not provided in the text
Delivery Location	Camperdown/Darlington, Sydney
Number of Units	2
Pre-Requisites	Not provided in the text
Lecturers	Not provided in the text

Multivariate Data Analysis多元数据分析的基础理论

Impacts on Estimation and Classification
The key assumptions for deriving the discriminant function are multivariate normality of the independent variables and unknown (but equal) dispersion and covariance structures (matrices) for the groups as defined by the dependent variable [7, 9]. Although the evidence is mixed regarding the sensitivity of discriminant analysis to violations of these assumptions, the researcher must always understand the impacts on the results that can be expected. Moreover, if the assumptions are violated and the potential remedies are not acceptable or do not address the severity of the problem, the researcher should consider alternative methods (e.g., logistic regression).

IDENTFYING ASSUMPTION VIOLATIONS Achieving univariate normality of individual variables will many times suffice to achieve multivariate normality. A number of tests for normality a e available to the researcher, along with the appropriate remedies, those most often being trans mations of the variables.

The issue of equal dispersion of the independent variables (i.e., equ valent covariance matrices) is similar to homoscedasticity between individual variables. The most common test is the Box’s $M$ test assessing the significance of differences in the matrices between the groups. Here the researcher is looking for a nonsignificant probability le el which would indicate that there were not differences between the group covariance matrices Given the sensitivity of the Box’s $M$ test, however, to the size of the covariance matrices a $d$ the number of groups in the analysis, researchers should use very conservative levels of significant differences (e.g., .01 rather than .05 ) when assessing whether differences are present. As the research design increases in sample size or terms of groups or number of independent variables, even more conservative levels of significance may be considered acceptabl

IMPACT ON ESTIMATION Data not meeting $t$ e multivariate normality assumption can cause problems in the estimation of the discriminant function. Remedies may be possible through transformations of the data to reduce the disparitie a ong the covariance matrices. However, in many instances these remedies are ineffectual. In these situations, the models should be thoroughly validated. If the dependent measure is binary, log stic regression should be used if at all possible.

IMPACT ON CASSIFCATION Unequal covariance matrices also negatively affect the classification process. If the sampl sizes are small and the covariance matrices are unequal, then the statistical significance of the estimation process is adversely affected. The more likely case is that of unequal covariances mong groups of adequate sample size, whereby observations are overclassified into the $\mathrm{g}$ oups with larger covariance matrices. This effect can be minimized by increasing the sample size and also by using the group-specific covariance matrices for classification purposes, but this approach mandates cross-validation of the discriminant results. Finally, quadratic classification techniques are available in many of the statistical programs if large differences exist between the covariance matrices of the groups and the remedies do not minimize the effect $[5,10,12]$.

对估计和分类的影响
导出判别函数的关键假设是自变量的多元正态性和因变量所定义的各组的未知（但相等）离散和协方差结构（矩阵）[7, 9]。虽然有关判别分析对违反这些假设的敏感性的证据不一，但研究人员必须始终了解这些假设对预期结果的影响。此外，如果违反了这些假设，而潜在的补救措施又不可接受或不能解决问题的严重性，研究人员应考虑采用其他方法（如逻辑回归）。

识别假设违反情况实现单变量的单变量正态性有时足以实现多变量正态性。研究人员可以使用多种正态性检验方法，并采取适当的补救措施，其中最常见的是变量的转换。

自变量的等离散性（即等价协方差矩阵）问题与单个变量之间的同方差性类似。最常见的检验是 Box’s $M$ 检验，用于评估组间矩阵差异的显著性。在这里，研究人员要寻找的是不显著的概率 le el，这将表明组间协方差矩阵之间不存在差异。鉴于方框 M$ 检验对协方差矩阵的大小和分析中的组数很敏感，研究人员在评估差异是否存在时，应使用非常保守的显著差异水平（如 0.01 而不是 0.05）。随着研究设计的样本量或组别或自变量数量的增加，甚至更保守的显著性水平也可以接受。

对估计的影响不符合多元正态性假设的数据会给判别函数的估计带来问题。可以通过数据转换来减少协方差矩阵之间的差异。然而，在许多情况下，这些补救措施都是无效的。在这种情况下，应该对模型进行彻底验证。如果因变量是二元的，则应尽可能使用对数回归。

对分类的影响不相等的协方差矩阵也会对分类过程产生负面影响。如果抽样规模较小，而协方差矩阵不相等，那么估计过程的统计意义就会受到不利影响。更有可能出现的情况是，在样本量足够大的组间，协方差不相等，观测值被过度分类到协方差矩阵较大的 $mathrm{g}$ 组中。这种影响可以通过增加样本量和使用特定组别的协方差矩阵来最小化，但这种方法需要对判别结果进行交叉验证。最后，如果各组的协方差矩阵之间存在较大差异，而补救措施又不能使这种效应最小化，那么许多统计程序都提供了二次分类技术[5,10,12]$。

Principal Components Analysis主成分分析法定义相关

2.3 Principal Components Using a Correlation Matrix
The derivation and properties of PCs considered above are based on the eigenvectors and eigenvalues of the covariance matrix. In practice, as will be seen in much of the remainder of this text, it is more common to define principal components as
$$
\mathbf{z}=\mathbf{A}^{\prime} \mathbf{x}^*
$$
where A now has columns consisting of the eigenvectors of the correlation matrix, and $\mathbf{x}^$ consists of standardized variables. The goal in adopting such an approach is to find the principal components of a standardized version $\mathbf{x}^$ of $\mathbf{x}$, where $\mathbf{x}^$ has $j$ th element $x_j / \sigma_{j j}^{1 / 2}, j=1,2, \ldots, p, x_j$ is the $j$ th element of $\mathbf{x}$, and $\sigma_{j j}$ is the variance of $x_j$. Then the covariance matrix for $\mathbf{x}^$ is the correlation matrix of $\mathbf{x}$, and the PCs of $\mathbf{x}^*$ are given by (2.3.1).

A third possibility, instead of using covariance or correlation matrices, is to use covariances of $x_j / w_j$, where the weights $w_j$ are chosen to reflect some a priori idea of the relative importance of the variables. The special case $w_j=\sigma_{j j}^{1 / 2}$ leads to $\mathbf{x}^*$, and to PCs based on the correlation matrix, but various authors have argued that the choice of $w_j=\sigma_{j j}^{1 / 2}$ is somewhat arbitrary, and that different values of $w_j$ might be better in some applications (see Section 14.2.1). In practice, however, it is relatively unusual that a uniquely appropriate set of $w_j$ suggests itself.

All the properties of the previous two sections are still valid for correlation matrices, or indeed for covariances based on other sets of weights, except that we are now considering PCs of $\mathrm{x}^*$ (or some other transformation of $\mathbf{x}$ ), instead of $\mathbf{x}$.

It might seem that the PCs for a correlation matrix could be obtained fairly easily from those for the corresponding covariance matrix, since $\mathbf{x}^$ is related to $\mathbf{x}$ by a very simple transformation. However, this is not the case; the eigenvalues and eigenvectors of the correlation matrix have no simple relationship with those of the corresponding covariance matrix. In particular, if the PCs found from the correlation matrix are expressed in terms of $\mathbf{x}$ by transforming back from $\mathbf{x}^$ to $\mathbf{x}$, then these PCs are not the same as the PCs found from $\boldsymbol{\Sigma}$, except in very special circumstances (Chatfield and Collins, 1989, Section 4.4). One way of explaining this is that PCs are invariant under orthogonal transformations of $\mathbf{x}$ but not, in general, under other transformations (von Storch and Zwiers, 1999, Section 13.1.10). The transformation from $\mathbf{x}$ to $\mathbf{x}^*$ is not orthogonal. The PCs for correlation and covariance matrices do not, therefore, give equivalent information, nor can they be derived directly from each other. We now discuss the relative merits of the two types of PC.

2.3 利用相关矩阵计算主成分
上文提到的主成分的推导和性质都是基于协方差矩阵的特征向量和特征值。在实践中，正如本文其余部分所述，更常见的是将主成分定义为
$$
\mathbf{z}=\mathbf{A}^{\prime} \mathbf{x}^*
$$
其中 A 的列由相关矩阵的特征向量组成，$\mathbf{x}^$ 由标准化变量组成。采用这种方法的目的是找到 $\mathbf{x}$ 的标准化版本 $\mathbf{x}^$ 的主成分、其中$mathbf{x}^$的第j个元素为$x_j / \sigma_{j j}^{1 / 2}, j=1,2, \ldots, p, x_j$是$mathbf{x}$的第j个元素，$\sigma_{j j}$是$x_j$的方差。那么 $\mathbf{x}^$ 的协方差矩阵就是 $\mathbf{x}$ 的相关矩阵，而 $\mathbf{x}^*$ 的 PCs 由 (2.3.1) 给出。

第三种可能是不使用协方差或相关矩阵，而是使用 $x_j / w_j$ 的协方差，其中权重 $w_j$ 的选择是为了反映变量相对重要性的某种先验想法。在特殊情况下，$w_j=\sigma_{j j}^{1 / 2}$ 会导致 $\mathbf{x}^*$，并导致基于相关矩阵的 PC，但不同作者认为，选择 $w_j=\sigma_{j j}^{1 / 2}$ 有些武断，在某些应用中，不同的 $w_j$ 值可能更好（见第 14.2.1 节）。然而，在实际应用中，一个唯一合适的 $w_j$ 值集并不常见。

前面两节中的所有性质对于相关矩阵或基于其他权重集的协方差仍然有效，只是我们现在考虑的是 $\mathrm{x}^*$（或 $\mathbf{x}$的其他变换）的 PC，而不是 $\mathbf{x}$。

看起来，相关矩阵的 PCs 可以很容易地从相应协方差矩阵的 PCs 中得到，因为 $mathbf{x}^$ 与 $mathbf{x}$ 是通过非常简单的变换得到的。然而，事实并非如此；相关矩阵的特征值和特征向量与相应协方差矩阵的特征值和特征向量没有简单的关系。特别是，如果通过从 $\mathbf{x}^$ 到 $\mathbf{x}$ 的变换，用 $\mathbf{x}$ 来表示从相关矩阵中发现的 PC，那么这些 PC 与从 $\boldsymbol{\Sigma}$ 中发现的 PC 并不相同，除非在非常特殊的情况下（Chatfield 和 Collins，1989 年，第 4.4 节）。解释这种情况的一种方法是，个人计算机在 $\mathbf{x}$ 的正交变换下是不变的，但在一般情况下，在其他变换下则不是（von Storch 和 Zwiers，1999 年，第 13.1.10 节）。从 $\mathbf{x}$ 到 $\mathbf{x}^*$ 的变换不是正交变换。因此，相关矩阵和协方差矩阵的 PCs 并不能提供等同的信息，也不能从彼此直接导出。现在我们来讨论一下这两种 PC 的相对优点。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

澳洲代写｜comp5318｜Machine Learning and Data Mining机器学习和数据挖掘悉尼大学

Posted on 2023年10月9日2023年10月9日 by statistics-lab

statistics-lab^TM为您悉尼大学（英语：The University of Sydney）Machine Learning and Data Mining机器学习和数据挖掘澳洲代写代考和辅导服务！

课程介绍：

澳洲代写｜comp5318｜Machine Learning and Data Mining机器学习和数据挖掘悉尼大学

Attribute	Detail
Course Code	MATH3205
Course Title	Further Topics in Operations Research
Coordinating Unit	School of Mathematics and Physics
Semester	Semester 2, 2023
Mode	In Person
Level	Undergraduate
Delivery Location	St Lucia
Number of Units	2
Pre-Requisites	MATH3202
Lecturers	Not provided in the text

Machine Learning and Data Mining机器学习和数据挖掘的基础理论

3.2.1 Classification accuracy and confusion matrix
The solution of each particular classification problem is a single class out of several $\left(m_0\right)$ possible classes. Classification accuracy and confusion matrix are frequently used to evaluate the quality of classifier’s solutions. Success of classification problem solutions is measured with classification accuracy. It can also be used for relational problems under the assumption that the relation membership is a two-class problem. Classification accuracy is defined as a relative frequency of correct classifications
$$
A c c=\frac{n_{\text {c:orT }}}{n} \cdot 100 \%
$$
with $n$ being the number of all possible examples for a given problem, and $n_{c o r r}$ the number of correctly classified examples by the current theory. The classification accuracy can be interpreted as a probability that a randomly selected example will be correctly classified.

In real-life problems it is virtually impossible to determine the exact classification accuracy because correct classifications of all examples are simply not known. Also $n$ is often large, if not infinite. Classification accuracy is therefore estimated from an independent testing set of solved examples, if available. Let $n_t$ be the number of testing examples. The classification accuracy is estimated with:
$$
A c c_t=\frac{n_{t, c o T T}}{n_t} \cdot 100 \%
$$
The testing set of examples must be independent of the learning set. Similarly, on the learning set the classification accuracy is estimated with:
$$
A c c_l=\frac{n_{l, f o r T}}{n_l} \cdot 100 \%
$$
This is an optimistic estimation (upper bound) of the classification accuracy. It is not difficult to build theories that achieve $A c c_l=100 \%$. It is sufficient to remember all learning examples and their (correct) solutions. Such theories perform well only on the learning set, and their $A c_l$ is usually a very poor estimation of the actual classification accuracy. Theories with $A c c_l \gg A c c_t$ overfit the learning set. Many machine learning algorithms require special techniques to prevent overfitting.

The lower bound of the classification accuracy is estimated with the majority class. The majority class is the most frequent class in the whole example space. Since the distribution of classes in example space is usually not known, it is estimated from the learning set. Let $n(C)$ be the number of learning examples from class $C$, and $n$ the number of all learning examples. The lowest acceptable classification accuracy (the default accuracy) can be trivially achieved by classifying all examples into the majority class:
$$
A c c_m=\max _C\left{\frac{n(C)}{n}\right} \cdot 100 \%
$$

3.2.1 分类准确率和混淆矩阵
每个特定分类问题的解决方案是多个 $\left(m_0\right)$ 可能类别中的一个类别。分类精度和混淆矩阵经常用于评估分类器解决方案的质量。分类问题解决方案的成功是用分类精度来衡量的。它也可以用于假设关系隶属度是二类问题的关系问题。分类准确度定义为正确分类的相对频率
$$
A c c=\frac{n_{\text {c:orT }}}{n} \cdot 100 \%
$$
其中 $n$ 是给定问题的所有可能示例的数量，$n_{c or r}$ 是当前理论正确分类的示例的数量。分类精度可以解释为随机选择的示例被正确分类的概率。

在现实生活中的问题中，几乎不可能确定准确的分类精度，因为根本不知道所有示例的正确分类。此外，$n$ 即使不是无限的，也通常很大。因此，分类准确性是根据已解决示例的独立测试集（如果有）来估计的。令 $n_t$ 为测试示例的数量。分类精度估计为：
$$
A c c_t=\frac{n_{t, c o T T}}{n_t} \cdot 100 \%
$$
测试示例集必须独立于学习集。类似地，在学习集上，分类精度估计为：
$$
A c c_l=\frac{n_{l, for T}}{n_l} \cdot 100 \%
$$
这是分类精度的乐观估计（上限）。建立实现 $A c c_l=100 \%$ 的理论并不困难。记住所有学习示例及其（正确）解决方案就足够了。此类理论仅在学习集上表现良好，并且它们的 $A c_l$ 通常对实际分类精度的估计非常差。 $A c c_l \gg A c c_t$ 的理论对学习集过度拟合。许多机器学习算法需要特殊的技术来防止过度拟合。

分类精度的下限是用多数类来估计的。多数类是整个示例空间中最常见的类。由于示例空间中类的分布通常是未知的，因此它是根据学习集估计的。令 $n(C)$ 为 $C$ 类的学习示例数量，$n$ 为所有学习示例的数量。通过将所有示例分类为多数类，可以轻松实现可接受的最低分类精度（默认精度）：
$$
A c c_m=\max _C\left{\frac{n(C)}{n}\right} \cdot 100 \%
$$

Rule-based algorithms基于规则的算法定义相关

1.3.6 Statistical Measures
In this thesis, some statistical measures are used as heuristics for development of rule learning algorithms and evaluation of rule quality. This subsection presents several measures namely entropy, J-measure, confidence, lift and leverage.

Entropy is introduced by Shannon in (Shanno, 1948), which is an information theoretic measure of uncertainty. Entropy $E$ can be calculated as illustrated in equation (1):
$$
E=-\sum_{i=0}^n p_i \cdot \log _2 p_i
$$
where $p$ is read as probability that an event occurs and $i$ is the index of the corresponding event.

J-measure is introduced in (Smyth \& Goodman, 1991), which is an information theoretic measure of average information content of a single rule. J-measure is essentially the product of two terms as illustrated in equation (2):
$$
J(Y, X=x)=P(x) \cdot j(Y, X=x)(2)
$$
where the first term $P(x)$ is read as the probability that the rule antecedent (left hand side) occurs and considered as a measure of simplicity (Smyth \& Goodman, 1992). In addition, the second term is read as j-measure, which is first introduced in (Blachman, 1968) but later modified in (Smyth \& Goodman, 1992) and considered as a measure of goodness of fit of a single rule (Smyth \& Goodman, 1992). The j-measure is calculated as illustrated in equation (3):
$$
j(Y, X=x)=P(y \mid x) \cdot \log _2\left(\frac{P(y \mid x)}{P(y)}\right)+(1-P(y \mid x)) \cdot \log _2\left(\frac{1-P(y \mid x)}{1-P(y)}\right)
$$
where $P(y)$ is read as prior probability that the rule consequent (right hand side) occurs and $P(y \mid x)$ is read as posterior probability that the rule consequent occurs given the rule antecedent as the condition.

In addition, j-measure has an upper bound referred to as jmax as indicated in (Smyth \& Goodman, 1992) and illustrated in equation (4):

1.3.6 统计测量
在本论文中，一些统计量被用作规则学习算法开发和规则质量评估的启发式方法。本小节将介绍几种统计量，即熵 (entropy)、J 值 (J-measure)、置信度 (cidence)、提升度 (lift) 和杠杆率 (leverage)。

熵是由香农在（Shanno，1948 年）中提出的，是不确定性的一种信息论度量。熵 $E$ 的计算公式如公式 (1) 所示：
$$
E=-\sum_{i=0}^n p_i \cdot \log _2 p_i
$$
其中，$p$ 表示事件发生的概率，$i$ 表示相应事件的索引。

J-measure 是在（Smyth \& Goodman, 1991）中引入的，它是对单条规则平均信息含量的一种信息论度量。J-measure 本质上是两个项的乘积，如公式 (2) 所示：
$$
J(Y, X=x)=P(x) \cdot j(Y, X=x)(2)
$$
其中，第一项 $P(x)$ 被理解为规则前件（左侧）出现的概率，并被视为简单性的衡量标准（Smyth \& Goodman, 1992）。此外，第二个项被理解为 j-measure，它最早是在（Blachman, 1968）中提出的，后来在（Smyth \& Goodman, 1992）中进行了修改，并被认为是对单一规则拟合度的一种度量（Smyth \& Goodman, 1992）。j-measure 的计算方法如公式 (3) 所示：
$$
j(Y, X=x)=P(y 中 x) \cdot \log _2\left(\frac{P(y 中 x)}{P(y)}\right)+(1-P(y 中 x)) \cdot \log _2\left(\frac{1-P(y \mid x)}{1-P(y)}\right)
$$
其中，$P(y)$ 表示规则结果（右侧）发生的先验概率，$P(y \mid x)$ 表示以规则前件为条件，规则结果发生的后验概率。

此外，j-measure 还有一个上限，称为 jmax，如（Smyth \& Goodman, 1992）所示，并在等式（4）中说明：

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

澳洲代写｜OLET2610｜Foundations of Quantum Computing量子计算的基础悉尼大学

Posted on 2023年10月9日2023年10月9日 by statistics-lab

statistics-lab^TM为您悉尼大学（英语：The University of Sydney）Foundations of Quantum Computing量子计算的基础澳洲代写代考和辅导服务！

课程介绍：

This OLE will provide a general introduction to the research field of quantum computing, covering hardware, software, and potential societal impact. The circuit model of quantum computing and example algorithms will be introduced, then building on this knowledge you will code and execute simple algorithms in a quantum software environment. Emphasis will be given to comparing quantum vs ‘classical’ performance of key algorithms. For hardware, the research challenges in developing quantum computer technology will be introduced, and you will undertake a critical analysis of specific hardware platforms (advantages and challenges). The potential societal impact of quantum computers, and quantum technologies more broadly, will be surveyed. On completion of this OLE, you will have gained an informed appreciation of this new technology and its potential impact, as well as generic skills that allow for the critical assessment and evaluation of potential new technologies.

澳洲代写｜OLET2610｜Foundations of Quantum Computing量子计算的基础悉尼大学

Attribute	Detail
Code	OLET2610
Academic Unit	Physics Academic Operations
Unit Name	Foundations of Quantum Computing
Credit Points	2
Pre-requisites	None mentioned in the provided text
Lecturers	Not explicitly mentioned in the text

Foundations of Quantum Computing量子计算的基础理论

1.4.3 Reduced Density Matrix
Consider a Hilbert space $\mathcal{H}=\mathcal{H}_A \oplus \mathcal{H}_B$. The reduced density matrix for system $A$ is defined as:
$$
\rho^A \equiv \operatorname{tr}_B\left(\rho^{A B}\right)
$$
$\operatorname{tr}_B$ is known as the partial trace of $\rho^{A B}$ over $B$. The partial trace is defined as :
$$
\operatorname{tr}_B\left(\left|a_1\right\rangle\left\langle a_1|| b_1\right\rangle\left\langle b_2\right|\right) \equiv\left|a_1\right\rangle\left\langle a_1\right| \operatorname{tr}\left(\left|b_1\right\rangle\left\langle b_2\right|\right)
$$
As we expect, if our state is just a tensor product a density matrix $\rho_A$ in $\mathcal{H}_A$ and a density matrix $\rho_B$ in $\mathcal{H}_B$ then
$$
\rho^A=\operatorname{tr}_B\left(\rho_A \rho_B\right)=\rho_A \operatorname{tr}\left(\rho_B\right)=\rho_A
$$
A less trivial example is the bell state.

1.4.6 Example: Infinite Square Well
As an example let us consider a particle sitting in a infinite square well with the state $\psi(x)=\sqrt{\frac{2}{\pi}} \sin (x), x \in[0, \pi]$. The density matrix is:
$$
\rho=\frac{2}{\pi} \sin x^{\prime} \sin x
$$
Now let us break the square well in half into two subspaces, $\mathcal{H}A \otimes \mathcal{H}_B$. Somewhat suprisingly, now we can calculate entropy and entanglement of these subspaces, even though the entire system is pure (and has zero entropy and entanglement). The key difference now is that in each subspace we no longer know if there is a particle or not. Thus, we must express each sub-Hilbert space in the basis $(|0\rangle+|1\rangle) \otimes \psi(x)$ where $|0\rangle$ represents no particle and $|1\rangle$ represents one particle. Equivalently, you can think of this as a way of breaking up the wave function into two functions. $$ \psi=|0,0\rangle \otimes|1, \psi(x)\rangle+|1, \psi(x)\rangle \otimes|0,0\rangle $$ Or, compressing notation and ignoring normalization for now, $$ \psi=|01\rangle+|10\rangle $$ Now we can find the reduced density matrix for $\mathcal{H}_A$. First we rewrite $\rho$ : $$ \begin{aligned} & \rho=(|01\rangle+|10\rangle)(\langle 01|+\langle 10|) \ & \rho=|01\rangle\langle 01|+| 10\rangle\langle 10|+| 10\rangle\langle 01|+| 01\rangle+\langle 10| \end{aligned} $$ The trace of $|10\rangle\langle 01|$ is zero since $\operatorname{tr}(|10\rangle\langle 01|)=\operatorname{tr}(\langle 01 \mid 10\rangle)=0$. We are left with $$ \begin{aligned} & \rho_A=\frac{2}{\pi} \sin x \sin y|1\rangle\left\langle 1\left|+\int{\pi / 2}^\pi \frac{2}{\pi} \sin (x)^2 d x\right| 0\right\rangle\langle 0| \
& \rho_A=\frac{2}{\pi} \sin x \sin y|1\rangle\left\langle 1\left|+\frac{1}{2}\right| 0\right\rangle\langle 0|
\end{aligned}
$$
To calculate the entropy of this subsystem we must know the eigenvalues of $\rho_A$. By inspection, it is clear that $|0\rangle$ is an eigenvector with eigenvalue $\frac{1}{2}$. We know the sum of the eigenvalues must be 1 , so the other eigenvalue is $\frac{1}{2}$. (Alternativly we could try $f(x)|1\rangle$ and work out the corresponding inner product, which is an integral.)
$$
S=-\operatorname{tr}(\rho \ln (\rho))=-\frac{1}{2} \ln \frac{1}{2}-\frac{1}{2} \ln \frac{1}{2}=\ln (2)
$$
This result could have been anticipated because there are two possibilities for measurement – we find the particle on the left or the right. Still, it is suprising that the entropy of a given subsystem can be non-zero while the entire system has zero entropy.

Quantum Algorithms 量子算法定义

the two possible states of the electron in classical physics. Many of the most counterintuitive aspects of quantum physics arise from the superposition principle which states that if a quantum system can be in one of two states, then it can also be in any linear superposition of those two states. For instance, the state of the electron could well be $\frac{1}{\sqrt{2}}|0\rangle+\frac{1}{\sqrt{2}}|1\rangle$ or $\frac{1}{\sqrt{2}}|0\rangle-\frac{1}{\sqrt{2}}|1\rangle$; or an infinite number of other combinations of the form $\alpha_0|0\rangle+\alpha_1|1\rangle$. The coefficient $\alpha_0$ is called the amplitude of state $|0\rangle$, and similarly with $\alpha_1$. And-if things aren’t already strange enough – the $\alpha$ ‘s can be complex numbers, as long as they are normalized so that $\left|\alpha_0\right|^2+\left|\alpha_1\right|^2=1$. For example, $\frac{1}{\sqrt{5}}|0\rangle+\frac{2 i}{\sqrt{5}}|1\rangle$ (where $i$ is the imaginary unit, $\sqrt{-1}$ ) is a perfectly valid quantum state! Such a superposition, $\alpha_0|0\rangle+\alpha_1|1\rangle$, is the basic unit of encoded information in quantum computers (Figure 10.1). It is called a qubit (pronounced “cubit”).
The whole concept of a superposition suggests that the electron does not make up its mind about whether it is in the ground or excited state, and the amplitude $\alpha_0$ is a measure of its inclination toward the ground state. Continuing along this line of thought, it is tempting to think of $\alpha_0$ as the probability that the electron is in the ground state. But then how are we to make sense of the fact that $\alpha_0$ can be negative, or even worse, imaginary? This is one of the most mysterious aspects of quantum physics, one that seems to extend beyond our intuitions about the physical world.

This linear superposition, however, is the private world of the electron. For us to get a glimpse of the electron’s state we must make a measurement, and when we do so, we get a single bit of information -0 or 1 . If the state of the electron is $\alpha_0|0\rangle+\alpha_1|1\rangle$, then the outcome of the measurement is 0 with probability $\left|\alpha_0\right|^2$ and 1 with probability $\left|\alpha_1\right|^2$ (luckily we normalized so $\left|\alpha_0\right|^2+\left|\alpha_1\right|^2=1$ ). Moreover, the act of measurement causes the system to change its state: if the outcome of the measurement is 0 , then the new state of the system is $|0\rangle$ (the ground state), and if the outcome is 1 , the new state is $|1\rangle$ (the excited state). Thisfeature of quantum physics, that a measurement disturbs the system and forces it to choose (in this case ground or excited state), is another strange phenomenon with no classical analog.

The superposition principle holds not just for 2-level systems like the one we just described, but in general for $k$-level systems. For example, in reality the electron in the hydrogen atom can be in one of many energy levels, starting with the ground state, the first excited state, the second excited state, and so on. So we could consider a $k$-level system consisting of the ground state and the first $k-1$ excited states, and we could denote these by $|0\rangle,|1\rangle,|2\rangle, \ldots,|k-1\rangle$. The superposition principle would then say that the general quantum state of the system is $\alpha_0|0\rangle+\alpha_1|1\rangle+\cdots+\alpha_{k-1}|k-1\rangle$, where $\sum_{j=0}^{k-1}\left|\alpha_j\right|^2=1$. Measuring the state of the system would now reveal a number between 0 and $k-1$, and outcome $j$ would occur with probability $\left|\alpha_j\right|^2$. As before, the measurement would disturb the system, and the new state would actually become $|j\rangle$ or the $j$ th excited state.

How do we encode $n$ bits of information? We could choose $k=2^n$ levels of the hydrogen atom. But a more promising option is to use $n$ qubits.

Let us start by considering the case of two qubits, that is, the state of the electrons of two hydrogen atoms. Since each electron can be in either the ground or excited state, in classical physics the two electrons have a total of four possible states-00, 01, 10, or 11-and are therefore suitable for storing 2 bits of information. But in quantum physics, the superposition principle tells us that the quantum state of the two electrons is a linear combination of the four classical states,
$$
|\boldsymbol{\alpha}\rangle=\alpha_{00}|00\rangle+\alpha_{01}|01\rangle+\alpha_{10}|10\rangle+\alpha_{11}|11\rangle,
$$

澳洲代写｜ECOS3022｜The Economics of Financial Markets金融市场经济学悉尼大学

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

澳洲代写｜COMP5328｜Advanced Machine Learning高级机器学习悉尼大学

Posted on 2023年10月9日2023年10月9日 by statistics-lab

statistics-lab^TM为您悉尼大学（英语：The University of Sydney）Advanced Machine Learning高级机器学习澳洲代写代考和辅导服务！

课程介绍：

Machine learning models explain and generalise data. This course introduces some fundamental machine learning concepts, learning problems and algorithms to provide understanding and simple answers to many questions arising from data explanation and generalisation. For example, why do different machine learning models work? How to further improve them? How to adapt them to different purposes?

澳洲代写｜COMP5328｜Advanced Machine Learning高级机器学习悉尼大学

Attribute	Detail
Year/Session	Semester 2, 2020
Code	COMP5328
Academic Unit	Computer Science
Unit Name	Advanced Machine Learning
Credit Points	6
Pre-requisites	None
Lecturers	Not explicitly mentioned in the text

Advanced Machine Learning高级机器学习理论

Definition: $\operatorname{AR}(p)$ model is a linear generative model based on the $p$ th order Markov assumption:
$$
\forall t, Y_t=\sum_{i=1}^p a_i Y_{t-i}+\epsilon_t
$$
where

$\epsilon_t \mathrm{~s}$ are zero mean uncorrelated random variables with variance $\sigma$.

$a_1, \ldots, a_p$ are autoregressive coefficients.

$Y_t$ is observed stochastic process.

Definition: the generalized autoregressive conditional heteroscedasticity $\operatorname{GARCH}(p, q)$ model is an $\operatorname{ARMA}(p, q)$ model for the variance $\sigma_t$ of the noise term $\epsilon_t$ :

$$\forall t, \sigma_{t+1}^2=\omega+\sum_{i=0}^{p-1} \alpha_i \sigma_{t-i}^2+\sum_{j=0}^{q-1} \beta_j \epsilon_{t-j}^2$$

where

$\epsilon_t \mathrm{~S}$ are zero mean Gaussian random variables with variance $\sigma_t$ conditioned on $\left{Y_{t-1}, Y_{t-2}, \ldots\right}$.

$\omega>0$ is the mean parameter.

Continuous state space version of Hidden Markov Models:

$$\begin{aligned}\mathbf{X}_{t+1} & =\mathbf{B X}_t+\mathbf{U}_t, \Y_t & =\mathbf{A} \mathbf{X}_t+\epsilon_t\end{aligned}$$where$\mathbf{X}_t$ is an $n$-dimensional state vector.$Y_t$ is an observed stochastic process.$\mathbf{A}$ and $\mathbf{B}$ are model parameters.$\mathbf{U}_t$ and $\epsilon_t$ are noise terms.

Different methods for estimating model parameters:

Maximum likelihood estimation:
Requires further parametric assumptions on the noise distribution (e.g. Gaussian).
Method of moments (Yule-Walker estimator).
Conditional and unconditional least square estimation.
Restricted to certain models.

Complexity and Generalisation复杂性和概括性定义

Given a space $Z$ and a fixed distribution $\left.D\right|Z$, let $S=\left{z_1, \ldots, z_m\right}$ be a set of examples drawn i.i.d. from $\left.D\right|_Z$. Furthermore, let $\mathcal{F}$ be a class of functions $f: Z \rightarrow \mathbb{R}$. Definition. The empirical Rademacher complexity of $\mathcal{F}$ is defined to be $$ \hat{R}_m(\mathcal{F})=\mathrm{E}\sigma\left[\sup {f \in \mathcal{F}}\left(\frac{1}{m} \sum{i=1}^m \sigma_i f\left(z_i\right)\right)\right]
$$
where $\sigma_1, \ldots, \sigma_m$ are independent random variables uniformly chosen from ${-1,1}$. We will refer to such random variables as Rademacher variables.
Definition. The Rademacher complexity of $\mathcal{F}$ is defined as
$$
R_m(\mathcal{F})=\mathrm{E}_D\left[\hat{R}_m(\mathcal{F})\right]
$$

Intuitively, the supremum measures, for a given set $S$ and Rademacher vector $\sigma$, the maximum correlation between $f\left(z_i\right)$ and $\sigma_i$ over all $f \in \mathcal{F}$. Taking the expectation over $\sigma$, we can then say that the empirical Rademacher complexity of $\mathcal{F}$ measures the ability of functions from $\mathcal{F}$ (when applied to a fixed set $S$ ) to fit random noise. The Rademacher complexity of $\mathcal{F}$ then measures the expected noise-fitting-ability of $\mathcal{F}$ over all data sets $S \in Z^m$ that could be drawn according to the distribution $\left.D\right|_Z$.

We note that Rademacher complexity can be defined even more generally on sets $A \subseteq \mathbb{R}^m$ by making the supremum over $a \in A$ (instead of $f \in \mathcal{F}$ ) and replacing each $f\left(z_i\right)$ with $a_i$. Taking $A=\mathcal{F}(S)={f(z) \mid f \in \mathcal{F}, z \in S}$ recovers the definition above. It will sometimes be convenient to use the more general definition.

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

Contingent claim economy或有债权经济的问题

Risk Allocation Principles风险分配原则定义

Computational complexity计算复杂度的问题

Euler–Fermat Theorem欧拉-费马定理定义

Applied Financial Econometrics应用金融计量经济学的问题

Applied Financial Econometrics应用金融计量经济学问题2

Complex Analysis (Advanced)进阶复杂分析的基础理论

Complex Analysis (Advanced)进阶复杂分析的定义相关

Financial Derivatives 金融衍生工具的基础理论

Fundamental theorem of asset pricing资产定价基本定理定义相关

Statistical Inference统计推断案例

Multivariate Data Analysis多元数据分析的基础理论

Principal Components Analysis主成分分析法定义相关

Machine Learning and Data Mining机器学习和数据挖掘的基础理论

Rule-based algorithms基于规则的算法定义相关

Foundations of Quantum Computing量子计算的基础理论

Quantum Algorithms 量子算法定义

Advanced Machine Learning高级机器学习理论

Complexity and Generalisation复杂性和概括性 定义

Complexity and Generalisation复杂性和概括性定义