assignmentutor™您的专属作业导师

assignmentutor-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。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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

## 统计代写|统计推断代写Statistical inference代考|HYPOTHESIS TESTING VIA EUCLIDEAN SEPARATION

In this section, we will be interested in testing hypotheses
$$H_{\ell}: P \in \mathcal{P}{\ell}, \ell=1, \ldots, L$$ on the probability distribution of a random observation $\omega$ in the situation where the families of distributions $\mathcal{P}{\ell}$ are obtained from a given family $\mathcal{P}$ of probability distributions by shifts. Specifically, we are given

• a family $\mathcal{P}$ of probability distributions on $\Omega=\mathbf{R}^{d}$ such that all distributions from $\mathcal{P}$ possess densities with respect to the Lebesgue measure on $\mathbf{R}^{n}$, and these densities are even functions on $\mathbf{R}^{d} ;{ }^{2}$
• a collection $X_{1}, \ldots, X_{L}$ of nonempty closed and convex subsets of $\mathbf{R}^{d}$, with at most one of the sets unbounded.

These data specify $L$ families $\mathcal{P}{\ell}$ of distributions on $\mathbf{R}^{d} ; \mathcal{P}{\ell}$ is comprised of distributions of random vectors of the form $x+\xi$, where $x \in X_{\ell}$ is deterministic, and $\xi$ is random with distribution from $\mathcal{P}$. Note that with this setup, deciding upon hypotheses (2.6) via observation $\omega \sim P$ is exactly the same as deciding, given observation
$$\omega=x+\xi,$$ where $x$ is a deterministic “signal” and $\xi$ is random noise with distribution $P$ known to belong to $\mathcal{P}$, on the “position” of $x$ w.r.t. $X_{1}, \ldots, X_{L}$, the $\ell$-th hypothesis $H_{\ell}$ saying that $x \in X_{\ell}$. The latter allows us to write down the $\ell$-th hypothesis as $H_{\ell}: x \in X_{\ell}$ (of course, this shorthand makes sense only within the scope of our current “signal plus noise” setup).

## 统计代写|统计推断代写Statistical inference代考|Testing Multiple Hypotheses via Euclidean separation

Situation. We are given $L$ nonempty and closed convex sets $X_{\ell} \subset \Omega=\mathbf{R}^{d}, 1 \leq \ell \leq$ $L$, with at least $L-1$ of the sets being bounded, and a spherical family of probability distributions $\mathcal{P}{\gamma}^{d}$. These data define $L$ families $\mathcal{P}{\ell}$ of probability distributions on $\mathbf{R}^{d}$, the family $\mathcal{P}{\ell}, 1 \leq \ell \leq L$, comprised of probability distributions of all random vectors of the form $x+\xi$, where deterministic $x$ (“signal”) belongs to $X{\ell}$, and $\xi$ is random noise with distribution from $\mathcal{P}{\gamma}^{d}$. Given positive integer $K$, we can speak about $L$ hypotheses on the distribution $P^{K}$ of $K$-repeated observation $\omega^{K}=$ $\left(\omega{1}, \ldots, \omega_{K}\right)$, with $\mathcal{H}{\ell}$ stating that $\omega^{K}$ is a quasi-stationary $K$-repeated observation associated with $\mathcal{P}{\ell}$. In other words $\mathcal{H}{\ell}=H{\ell}^{\otimes, K}$; see Section 2.1.3.3. Finally, we are given a closeness $\mathcal{C}$.

Our goal is to decide on the hypotheses $\mathcal{H}{1}, \ldots, \mathcal{H}{L}$ up to closeness $\mathcal{C}$ via $K$ repeated observation $\omega^{K}$. Note that this is a natural extension of the case $\mathbf{Q S}$ of pairwise testing from repeated observations considered in Section $2.2 .3$ (there $L=2$ and $\mathcal{C}$ is the only meaningful closeness on a two-hypotheses set: $\left(\ell, \ell^{\prime}\right) \in \mathcal{C}$ if and only if $\ell=\ell^{\prime}$ ).

The Standing Assumption which we assume to hold by default everywhere in this section is:
Whenever $\ell, \ell^{\prime}$ are not $\mathcal{C}$-close: $\left(\ell, \ell^{\prime}\right) \notin \mathcal{C}$, the sets $X_{\ell}, X_{\ell^{\prime}}$ do not intersect.
Strategy: We intend to attack the above testing problem by assembling pairwise Euclidean separation Majority tests via the construction from Section 2.2.4.3.
Building blocks to be assembled are Euclidean separation $K$-observation pairwise Majority tests constructed for the pairs $\mathcal{H}{\ell}, \mathcal{H}{\ell^{\prime}}$ of hypotheses with $\ell$ and $\ell^{\prime}$ not close to each other, that is, with $\left(\ell, \ell^{\prime}\right) \notin \mathcal{C}$. These tests are built as explained in Section 2.2.3.2; for the reader’s convenience, here is the construction. For a pair $\left(\ell, \ell^{\prime}\right) \notin \mathcal{C}$, we

1. Find the optimal value $\mathrm{Opt}{\ell \ell^{\prime}}$ and an optimal solution $\left(u{\ell f \prime}, v_{\ell f^{\prime}}\right)$ to the convex optimization problem
$$\mathrm{Opt}{\ell \ell^{\prime}}=\min {u \in X_{\ell, v \in X_{\ell^{\prime}}}} \frac{1}{2}|u-v|_{2} .$$

# 统计推断代考

## 统计代写|统计推断代写Statistical inference代考|HYPOTHESIS TESTING VIA EUCLIDEAN SEPARATION

$$H_{\ell}: P \in \mathcal{P} \ell, \ell=1, \ldots, L$$

• 一个家庭 $\mathcal{P}$ 的概率分布 $\Omega=\mathbf{R}^{d}$ 这样所有的分布 $\mathcal{P}$ 具有关于 Lebesgue 测度的密度 $\mathbf{R}^{n}$ ，这些密度甚至是函数 $\mathbf{R}^{d} ;{ }^{2}$
• 一个集合 $X_{1}, \ldots, X_{L}$ 的非空闭凸子集 $\mathbf{R}^{d}$ ，至多有一组无界。
这些数据说明 $L$ 家庭 $\mathcal{P} \ell$ 分布在 $\mathbf{R}^{d} ; \mathcal{P} \ell$ 由以下形式的随机向量的分布组成 $x+\xi$ ，在哪里 $x \in X_{\ell}$ 是确定性的，并且 $\xi$ 是随机的，分布来自 $\mathcal{P}$. 请注意，使用此设置， 通过观䕓决定假设 (2.6) $\omega \sim P$ 与决定完全相同，给定观䕓
$$\omega=x+\xi,$$
在哪里 $x$ 是一个确定性的”信号”，并且 $\xi$ 是具有分布的随机橾声 $P$ 已知属于 $\mathcal{P}$ ，关于”位置”的 $x$ 写 $X_{1}, \ldots, X_{L}$ ，这 $\ell$-第假设 $H_{\ell}$ 这么说 $x \in X_{\ell}$. 后者允许我们写下缆弜 假设为 $H_{\ell}: x \in X_{\ell}$ (当然，这种简写只在我们当前的”信号加噪声“设置范围内才有意义）。

## 统计代写|统计推断代写Statistical inference代考|Testing Multiple Hypotheses via Euclidean separation

1. 找到最优值 $\mathrm{Opt} \ell \ell^{\prime}$ 和最优解 $\left(u \ell f \prime, v_{\ell f^{\prime}}\right)^{\text {到凸优化问题 }}$
$$\operatorname{Opt} \ell \ell^{\prime}=\min u \in X_{\ell, v \in X_{\ell}} \frac{1}{2}|u-v|_{2} .$$

## 有限元方法代写

assignmentutor™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。

## 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。

assignmentutor™您的专属作业导师
assignmentutor™您的专属作业导师