assignmentutor-lab™ 为您的留学生涯保驾护航 在代写基础数据分析Elementary data Analysis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。我们的专家在代写基础数据分析Elementary data Analysis代写方面经验极为丰富，各种基础数据分析Elementary data Analysis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
assignmentutor™您的专属作业导师

## 数学代写|基础数据分析代写Elementary data Analysis代考|k-Nearest-Neighbor Regression

At the other extreme from ignoring the distance between $x_i$ and $x$, we could do nearest-neighbor regression:
$$\widehat{w}\left(x_i, x\right)= \begin{cases}1 & x_i \text { nearest neighbor of } x \ 0 & \text { otherwise }\end{cases}$$
This is very sensitive to the distance between $x_i$ and $x$. If $\mu(x)$ does not change too rapidly, and $X$ is pretty thoroughly sampled, then the nearest neighbor of $x$ among the $x_i$ is probably close to $x$, so that $\mu\left(x_i\right)$ is probably close to $\mu(x)$. However, $y_i=$ $\mu\left(x_i\right)+$ noise, so nearest-neighbor regression will include the noise into its prediction. We might instead do $k$-nearest neighbor regression,
$$\widehat{w}\left(x_i, x\right)=\left{\begin{array}{cl} 1 / k & x_i \text { one of the } k \text { nearest neighbors of } x \ 0 & \text { otherwise } \end{array}\right.$$
Again, with enough samples all the $k$ nearest neighbors of $x$ are probably close to $x$, so their regression functions there are going to be close to the regression function at $x$. But because we average their values of $y_i$, the noise terms should tend to cancel each other out. As we increase $k$, we get smoother functions $-$ in the limit $k=n$ and we just get back the constant. Figure $1.5$ illustrates this for our running example data. ${ }^{10}$ To use $k$-nearest-neighbors regression, we need to pick $k$ somehow. This means we need to decide how much smoothing to do, and this is not trivial. We will return to this point in Chapter 3 .

Because $k$-nearest-neighbors averages over only a fixed number of neighbors, each of which is a noisy sample, it always has some noise in its prediction, and is generally not consistent. This may not matter very much with moderately-large data (especially once we have a good way of picking $k$ ). If we want consistency, we need to let $k$ grow with $n$, but not too fast; it’s enough that as $n \rightarrow \infty, k \rightarrow \infty$ and $k / n \rightarrow 0$ (Györfi et al., 2002, Thm. 6.1, p. 88).

## 数学代写|基础数据分析代写Elementary data Analysis代考|Kernel Smoothers

Changing $k$ in a $k$-nearest-neighbors regression lets us change how much smoothing we’re doing on our data, but it’s a bit awkward to express this in terms of a number of data points. It feels like it would be more natural to talk about a range in the independent variable over which we smooth or average. Another problem with $k$ $\mathrm{NN}$ regression is that each testing point is predicted using information from only a few of the training data points, unlike linear regression or the sample mean, which always uses all the training data. It’d be nice if we could somehow use all the training data, but in a location-sensitive way.

There are several ways to do this, as we’ll see, but a particularly useful one is kernel smoothing, a.k.a. kernel regression or Nadaraya-Watson regression. To begin with, we need to pick a kernel function ${ }^{11} K\left(x_i, x\right)$ which satisfies the following properties:

1. $K\left(x_i, x\right) \geq 0$
2. $K\left(x_i, x\right)$ depends only on the distance $x_i-x$, not the individual arguments
3. $\int x K(0, x) d x=0$
4. $0<\int x^2 K(0, x) d x<\infty$
These conditions together (especially the last one) imply that $K\left(x_i, x\right) \rightarrow 0$ as $\mid x_i-$ $x \mid \rightarrow \infty$. Two examples of such functions are the density of the Unif $(-b / 2, h / 2)$ distribution, and the density of the standard Gaussian $\mathscr{N}(0, \sqrt{h})$ distribution. Here $b$ can be any positive number, and is called the bandwidth.

# 基础数据分析代考

## 数学代写|基础数据分析代写基本数据分析代考|k-Nearest-Neighbor – Regression

. . data- Analysis

$$\widehat{w}\left(x_i, x\right)= \begin{cases}1 & x_i \text { nearest neighbor of } x \ 0 & \text { otherwise }\end{cases}$$这是非常敏感的距离 $x_i$ 和 $x$。如果 $\mu(x)$ 变化不会太快，而且 $X$ 都是经过充分采样的，那么最近的邻居是 $x$ 在 $x_i$ 可能接近于 $x$，因此 $\mu\left(x_i\right)$ 可能接近于 $\mu(x)$。然而， $y_i=$ $\mu\left(x_i\right)+$ 噪声，所以最近邻回归将包括噪声到它的预测。我们可能会做 $k$-nearest neighbor regression，
$$\widehat{w}\left(x_i, x\right)=\left{\begin{array}{cl} 1 / k & x_i \text { one of the } k \text { nearest neighbors of } x \ 0 & \text { otherwise } \end{array}\right.$$

. conf

## 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。