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• 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|统计与机器学习作业代写Statistical and Machine Learning代考|Types of Statistical Machine Learning Models

Statistical machine learning models are most commonly classified as parametric models, semiparametric models, and nonparametric models. Next, we define each type of statistical machine learning models and provide examples that help to understand each one.

Parametric Model It is a type of statistical machine learning model in which all the predictors take predetermined forms with the response. Linear models (e.g., multiple regression: $y=\beta_1 x_1+\beta_2 x_2+\beta_3 x_3+\epsilon$ ), generalized linear models [Poisson regression: $E(y \mid x)=\exp \left(\beta_1 x_1+\beta_2 x_2+\beta_3 x_3\right)$ ], and nonlinear models (nonlinear regression: $y=\beta_1 x_1+\beta_2 x_2+\beta_3 e^{\beta_4 x_3}+\epsilon$ ) are examples of parametric statistical machine learning models because we know the function that describes the relationship between the response and the explanatory variables. These models are very easy to interpret but very inflexible.

Nonparametric Model It is a type of statistical machine learning model in which none of the predictors take predetermined forms with the response but are constructed according to information derived from data. Two common statistical machine learning models are kernel regression and smoothing spline. Kernel regression estimates the conditional expectation of $y$ at a given value $x$ using a weighted filter on the data $\left(y=m(x)+\epsilon\right.$, with $\left.\widehat{m}\left(x_0\right)=\frac{\sum_{i=1}^n K\left(\frac{x_i-x_0}{h}\right) y_i}{\sum_{i=1}^n K\left(\frac{x_i-x_0}{h}\right)}\right)$, where $h$ is the bandwidth (this estimator of $m(x)$ is called the Nadaraya-Watson $(N W)$ kernel estimator) and $K$ is a kernel function. While smoothing splines minimize the sum of squared residuals plus a term which penalizes the roughness of the fit $\left[y=\beta_0+\beta_1 x+\beta_2 x^2+3 x^3+\sum_{j=1}^J \beta_{1 j}\left(x-\theta_j\right){+}^3\right.$, where $\left(x-\theta_j\right){+}=x-\theta_j$, $x>\theta_j$ and 0 otherwise], this model in brackets is a spline of degree 3 which is represented as a power series. These models are very difficult to interpret but are very flexible. Nonparametric statistical machine learning models differ from parametric models in that the shape of the functional relationships between the response (dependent) and the explanatory (independent) variables are not predetermined but can be adjusted to capture unusual or unexpected features of the data. Nonparametric between estimated and true values) by imposing no specific model structure other than certain smoothness assumptions, and therefore they are particularly useful when than certain smoothness assumptions, and therefore they are particularly useful when we have little information or we want to be flexible about the underlying statistical machine learning model. In general, nonparametric statistical machine learning models are very flexible and are better at fitting the data than parametric statistical machine learning models. However, these models require larger samples than parametric statistical machine learning models because the data must supply the model structure as well as the model estimates.

## 统计代写|统计与机器学习作业代写Statistical and Machine Learning代考|Model Effects

Many statistical machine learning models are expressed as models that incorporate fixed effects, which are parameters associated with an entire population or with certain levels of experimental factors of interest. Other models are expressed as random effects, where individual experimental units are drawn at random from a population, while a model with fixed effects and random effects is called a mixedeffects model (Pinheiro and Bates 2000).

According to Milliken and Johnson (2009), a factor is a random effect if its levels consist of a random sample of levels from a population of possible levels, while a factor is a fixed effect if its levels are selected by a nonrandom process or if its levels consist of the entire population of possible levels.

Mixed-effects models, also called multilevel models in the social science community (education, psychology, etc.), are an extension of regression models that allow for the incorporation of random effects; they are better suited to describe relationships between a response variable and some covariates in data that are grouped according to one or more classification factors. Examples of such grouped data include longitudinal data, repeated measures data, multilevel data, and block designs. One example of grouped data are animals that belong to the same herd; for example, assume we have 10 herds with 50 animals (observations) in each. By associating to observations (animals) sharing the same level of a classification factor (herd) a common random effect, mixed-effects models parsimoniously represent the covariance structure induced by the grouping of data (Pinheiro and Bates 2000). Most of the early work on mixed models was motivated by the animal science community driven by the need to incorporate heritabilities and genetic correlations in parsimonious fashion.

Next we provide an example to illustrate how to build these types of models. Assume that five environments were chosen at random from an agroecological area of Mexico. Then in each area, three replicates of a new variety (NV) of maize were tested to measure grain yield (GY) in tons per hectare. The data collected from this experiment are shown in Fig. 1.2.

Since the only factor that changes among the observations measured in this experiment is the environment, they are arranged in a one-way classification because they are classified according to a single characteristic: the environments in which the observations were made (Pinheiro and Bates 2000 ). The data structure is very simple since each row represents one observation for which the environment and GY were recorded, as can be seen in Table 1.1.

# 统计与机器学习代考

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## 有限元方法代写

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## 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
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