统计代写|统计推断作业代写statistical inference代考|Theories of Estimation

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statistics-lab™ 为您的留学生涯保驾护航 在代写统计推断statistical inference方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写统计推断statistical inference代写方面经验极为丰富,各种代写统计推断statistical inference相关的作业也就用不着说。

我们提供的统计推断statistical inference及其相关学科的代写,服务范围广, 其中包括但不限于:

  • Statistical Inference 统计推断
  • Statistical Computing 统计计算
  • Advanced Probability Theory 高等楖率论
  • Advanced Mathematical Statistics 高等数理统计学
  • (Generalized) Linear Models 广义线性模型
  • Statistical Machine Learning 统计机器学习
  • Longitudinal Data Analysis 纵向数据分析
  • Foundations of Data Science 数据科学基础
A Gentle Introduction to Bayesian Belief Networks
统计代写|统计推断作业代写statistical inference代考|Theories of Estimation

统计代写|统计推断作业代写statistical inference代考|ELEMENTS OF POINT ESTIMATION

Essentially there are three stages of sophistication with regard to estimation of a parameter:

  1. At the lowest level-a simple point estimate;
  2. At a higher level-a point estimate along with some indication of the error of that estimate;
  3. At the highest level-one conceives of estimating in terms of a “distribution” or probability of some sort of the potential values that can occur.

This entails the specification of some set of values presumably more restrictive than the entire set of values that the parameter can take on or relative plausibilities of those values or an interval or region.

Consider the I.Q. of University of Minnesota freshmen by taking a random sample of them. We could be satisfied with the sample average as reflective of that population. More insight, however, may be gained by considering the variability

of scores by estimating a variance. Finally one might decide that a highly likely interval for the entire average of freshmen would be more informative.

Sometimes a point estimate is about all you can do. Representing distances on a map, for example. At present there is really no way of reliably illustrating a standard error on a map-so a point estimate will suffice.

An “estimate” is a more or less reasonable guess at the true value of a magnitude or parameter or even a potential observation, and we are not necessarily interested in the consequences of estimation. We may only be concerned in what we should believe a true value to be rather than what action or what the consequences are of this belief. At this point we separate estimation theory from decision theory, though in many instances this is not the case.

统计代写|统计推断作业代写statistical inference代考|POINT ESTIMATION

  1. An estimate might be considered “good” if it is in fact close to the true value on average or in the long run (pre-trial).
  2. An estimate might be considered “good” if the data give good reason to believe the estimate will be close to the true value (post trial).
    A system of estimation will be called an estimator
  3. Choose estimators which on average or very often yield estimates which are close to the true value.
  4. Choose an estimator for which the data give good reason to believe it will be close to the true value that is, a well-supported estimate (one that is suitable after the trials are made.)

With regard to the first type of estimators we do not reject one (theoretically) if it gives a poor result (differs greatly from the true value) in a particular case (though you would be foolish not to). We would only reject an estimation procedure if it gives bad results on average or in the long run. The merit of an estimator is judged, in general, by the distribution of estimates it gives rise to-the properties of its sampling distribution. One property sometimes stressed is unbiasedness. If

$T(D)$ is the estimator of $\theta$ then unbiasedness requires
E[T(D)]=\theta .
For example an unbiased estimator of a population variance $\sigma^{2}$ is
(n-1)^{-1} \sum\left(x_{i}-\bar{x}\right)^{2}=s^{2}
since $E\left(s^{2}\right)=\sigma^{2}$.
Suppose $Y_{1}, Y_{2}, \ldots$ are i.i.d. Bernoulli random variables $P\left(Y_{i}=1\right)=\theta$ and we sample until the first “one” comes up so that probability that the first one appears after $X=x$ zeroes is
P(X=x \mid \theta)=\theta(1-\theta)^{x} \quad x=0,1, \ldots \quad 0<\theta<1 . $$ Seeking an unbiased estimator we have $$ \theta=E(T(Y))=\sum_{x=0}^{\infty} t(x) \theta(1-\theta)^{x}=t(0) \theta+t(1) \theta(1-\theta)+\cdots . $$ Equating the terms yields the unique solution $t(0)=1, t(x)=0$ for $x \geq 1$. This is flawed because this unique estimator always lies outside of the range of $\theta$. So unbiasedness alone can be a very poor guide. Prior to unbiasedness we should have consistency (which is an asymptotic type of unbiasedness, but considerably more). Another desideratum that many prefer is invariance of the estimation procedure. But if $E(X)=\theta$, then for $g(X)$ a smooth function of $X, E(g(X)) \neq g(\theta)$ unless $g(\cdot)$ is linear in $X$. Definitions of classical and Fisher consistency follow: Consistency: An estimator $T_{n}$ computed from a sample of size $n$ is said to be a consistent estimator of $\theta$ if for any arbitrary $\epsilon>0$ and $\delta>0$ there is some value, $N$, such that
P\left[\left|T_{n}-\theta\right|<\epsilon\right]>1-\delta \quad \text { for all } n>N,

统计代写|统计推断作业代写statistical inference代考|Fisher’s Definition of Consistency for i.i.d. Random Variables

“A function of the observed frequencies which takes on the exact parametric value when for those frequencies their expectations are substituted.”

For a discrete random variable with $P\left(X_{j}=x_{j} \mid \theta\right)=p_{j}(\theta)$ let $T_{n}$ be a function of the observed frequencies $n_{j}$ whose expectations are $E\left(n_{j}\right)=n p_{j}(\theta)$. Then the linear function of the frequencies $T_{n}=\frac{1}{n} \sum_{j} c_{j} n_{j}$ will assume the value
\tau(\theta)=\Sigma c_{j} p_{j}(\theta)
when $n p_{j}(\theta)$ is substituted for $n_{j}$ and thus $n^{-1} T_{n}$ is a consistent estimator of $\tau(\theta)$.
Another way of looking at this is:
Let $F_{n}(x)=\frac{1}{n} \times #$ of observations $\leq x$
=\frac{i}{n} \text { for } x_{(i-1)}<x \leq x_{(i)}
where $x_{(j)}$ is the $j$ th smallest observation. If $T_{n}=g\left(F_{n}(x)\right)$ and $g(F(x \mid \theta))=\tau(\theta)$ then $T_{n}$ is Fisher consistent for $\tau(\theta)$. Note if
T_{n}=\int x d F_{n}(x)=\bar{x}{n} $$ and if $$ g(F)=\int x d F(x)=\mu $$ then $\bar{x}{n}$ is Fisher consistent for $\mu$.
On the other hand, if $T_{n}=\bar{x}{n}+\frac{1}{n}$, then this is not Fisher consistent but is consistent in the ordinary sense. Fisher Consistency is only defined for i.i.d. $X{1}, \ldots, X_{n}$.
However, as noted by Barnard (1974), “Fisher consistency can only with difficulty be invoked to justify specific procedures with finite samples” and also “fails because not all reasonable estimates are functions of relative frequencies.” He also presents an estimating procedure that does meet his requirements that the estimate lies within the parameter space and is invariant based on pivotal functions.

A Bayesian Network approach to diagnosing the root cause of failure from  trouble tickets
统计代写|统计推断作业代写statistical inference代考|Theories of Estimation


统计代写|统计推断作业代写statistical inference代考|ELEMENTS OF POINT ESTIMATION


  1. 在最低层——简单的点估计;
  2. 在更高的层次上——一个点估计以及该估计错误的一些指示;
  3. 在最高级别,第一级设想根据可能发生的某种潜在值的“分布”或概率进行估计。






统计代写|统计推断作业代写statistical inference代考|POINT ESTIMATION

  1. 如果实际上平均或长期(预审)接近真实值,则估计值可能被认为是“好”的。
  2. 如果数据有充分的理由相信估计值将接近真实值(试验后),则估计值可能被认为是“好的”。
  3. 选择平均或经常产生接近真实值的估计值的估计器。
  4. 选择一个数据有充分理由相信它会接近真实值的估计量,即一个有充分支持的估计值(在进行试验后适合的估计值。)


磷(X=X∣θ)=θ(1−θ)XX=0,1,…0<θ<1.寻求一个无偏估计我们有θ=和(吨(是))=∑X=0∞吨(X)θ(1−θ)X=吨(0)θ+吨(1)θ(1−θ)+⋯.相等的项产生唯一的解决方案吨(0)=1,吨(X)=0为了X≥1. 这是有缺陷的,因为这个唯一的估计量总是在θ. 因此,仅凭公正可能是一个非常糟糕的指南。在无偏性之前,我们应该具有一致性(这是一种渐近类型的无偏性,但要多得多)。许多人更喜欢的另一个要求是估计过程的不变性。但如果和(X)=θ,那么对于G(X)的平滑函数X,和(G(X))≠G(θ)除非G(⋅)是线性的X. 经典一致性和 Fisher 一致性的定义如下: 一致性:估计量吨n根据大小样本计算n据说是一致的估计量θ如果对于任何任意ε>0和d>0有一定的价值,ñ, 这样
磷[|吨n−θ|<ε]>1−d 对全部 n>ñ,

统计代写|统计推断作业代写statistical inference代考|Fisher’s Definition of Consistency for i.i.d. Random Variables


对于离散随机变量磷(Xj=Xj∣θ)=pj(θ)让吨n是观测频率的函数nj谁的期望是和(nj)=npj(θ). 然后是频率的线性函数吨n=1n∑jCjnj将假定值
让F_{n}(x)=\frac{1}{n} \times #F_{n}(x)=\frac{1}{n} \times #观察≤X
=一世n 为了 X(一世−1)<X≤X(一世)
在哪里X(j)是个j最小的观察。如果吨n=G(Fn(X))和G(F(X∣θ))=τ(θ)然后吨n费雪是否一致τ(θ). 注意如果
另一方面,如果吨n=X¯n+1n,那么这不是Fisher一致,而是通常意义上的一致。Fisher 一致性仅针对 iid 定义X1,…,Xn.
然而,正如 Barnard (1974) 所指出的,“Fisher 一致性很难被用来证明具有有限样本的特定程序”并且“失败,因为并非所有合理的估计都是相对频率的函数”。他还提出了一个估计程序,该程序确实满足了他的要求,即估计值位于参数空间内并且基于关键函数是不变的。

统计代写|统计推断作业代写statistical inference代考 请认准statistics-lab™

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在概率论概念中,随机过程随机变量的集合。 若一随机系统的样本点是随机函数,则称此函数为样本函数,这一随机系统全部样本函数的集合是一个随机过程。 实际应用中,样本函数的一般定义在时间域或者空间域。 随机过程的实例如股票和汇率的波动、语音信号、视频信号、体温的变化,随机运动如布朗运动、随机徘徊等等。


贝叶斯统计概念及数据分析表示使用概率陈述回答有关未知参数的研究问题以及统计范式。后验分布包括关于参数的先验分布,和基于观测数据提供关于参数的信息似然模型。根据选择的先验分布和似然模型,后验分布可以解析或近似,例如,马尔科夫链蒙特卡罗 (MCMC) 方法之一。贝叶斯统计概念及数据分析使用后验分布来形成模型参数的各种摘要,包括点估计,如后验平均值、中位数、百分位数和称为可信区间的区间估计。此外,所有关于模型参数的统计检验都可以表示为基于估计后验分布的概率报表。





随着AI的大潮到来,Machine Learning逐渐成为一个新的学习热点。同时与传统CS相比,Machine Learning在其他领域也有着广泛的应用,因此这门学科成为不仅折磨CS专业同学的“小恶魔”,也是折磨生物、化学、统计等其他学科留学生的“大魔王”。学习Machine learning的一大绊脚石在于使用语言众多,跨学科范围广,所以学习起来尤其困难。但是不管你在学习Machine Learning时遇到任何难题,StudyGate专业导师团队都能为你轻松解决。


基础数据: $N$ 个样本, $P$ 个变量数的单样本,组成的横列的数据表
变量定性: 分类和顺序;变量定量:数值
数学公式的角度分为: 因变量与自变量


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。


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 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。



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