《回归分析》 - 武萍、吴贤毅 - 清华大学出版社 - 香港大書城

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『簡體書』回归分析

書城自編碼： 2886599
分類：簡體書→大陸圖書→教材→研究生/本科/专科教材
作者：武萍、吴贤毅
國際書號(ISBN)： 9787302446309
出版社：清华大学出版社
出版日期： 2016-08-01
版次： 1 印次： 1

書度/開本： 16开釘裝：平装

售價：HK$ 58.5

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編輯推薦：

本书内容能够分为三部分：（1）线性回归分析所需要的矩阵代数理论、多元正态分布；（2）线性回归的基本利率和方法，包括线性估计的一般小样本理论、关于线性线性假设的F-检验方法、基于线性模型的方差分析理论、变量选择问题的讨论、共线性问题、异常值问题以及Box-Cox模型等与线性回归相关的内容；（3）用于分类响应变量的Logist回归模型的基本理论和方法。本书要求读者具有高等代数（或者线性代数）和概率论与数理统计的良好基础。本书的特点之一是在尽可能少的基础知识要求下讲清回归分析的理论问题，同事，本书也附带了一些SAS代码，这将有助于实际应用中的数据处理。本书可供统计学专业、数学专业或者其他相关专业作为本科生回归分析课程教材使用，也可作为非统计学专业的研究人员学习回归分析基础理论的参考使用。

內容簡介：

本书内容分为三部分：1?线性回归分析所需要的矩阵理论、多元正态分布；2?线性回归的基本理论和方法，包括线性估计的一般小样本理论、关于线性假设的?F-检验方法、基于线性模型的方差分析理论、变量选择问题的讨论、共线性问题、异常值问题以及?Box-Cox?模型等与线性回归相关的内容；3?用于分类响应变量的Logist回归模型的基本理论和方法。
本书要求读者具有高等代数或者线性代数和概率论与数理统计的良好基础。本书的特点之一是在尽可能少的基础知识要求下讲清线性回归分析的理论问题，同时，本书也附带了一些SAS代码，这将有助于实际应用中的数据处理。
本书可供统计学专业、数学专业或者其他相关专业作为本科生回归分析课程教材使用，也可作为非统计学专业的研究人员学习回归分析基础理论的参考书使用。

關於作者：

吴贤毅：华东师范大学金融与统计学院教授，博士生导师，研究领域包括随机调度，概率统计，非寿险精算，在随机调度，概率统计以及非寿险精算的国际主流杂志发表过数十篇学术研究论文，在随机调度方面的研究获得过三次国家自然科学基金资助，其在随机调度方面的研究成果发表于Operations Research,European
Journal of Operations Research,Journal of Scheduling 等。

Contents

Chapter 1 Preliminaries: Matrix Algebra and Random Vectors ........ 1

1.1 Preliminary matrix algebra
............................................................ 1

1.1.1 Trace and eigenvalues..........................................................
1

1.1.2 Symmetric
matrices............................................................. 3

1.1.3 Idempotent matrices and orthogonal projection..................... 6

1.1.4 Singular value decomposition
............................................... 9

1.1.5 Vector di.erentiation and generalized inverse
.......................10

1.1.6 Exercises ...........................................................................10

1.2 Expectation and
covariance...........................................................11

1.2.1 Basic properties
.................................................................11

1.2.2 Mean and variance of quadratic forms
.................................12

1.2.3 Exercises
...........................................................................14

1.3 Moment generating functions and independence
.............................16

1.3.1 Exercises
...........................................................................17

Chapter 2 Multivariate Normal
Distributions.....................................18

2.1 De.nitions and fundamental results
...............................................18

2.2 Distribution of quadratic forms
.....................................................25

2.3 Exercises......................................................................................27

Chapter 3 Linear Regression Models
...................................................29

3.1 Introduction.................................................................................29

3.2 Regression interpreted as conditional mean
....................................31

3.3 Linear regression interpreted as linear prediction
............................33

3.4 Some nonlinear
regressions............................................................34

3.5 Typical data structure of linear regression models
..........................35

3.6 Exercises......................................................................................36

Chapter 4 Estimation and Distribution Theory
..................................38

4.1 Least squares estimation LSE .....................................................38

4.1.1 Motivation: why is LS
reasonable........................................38

Regression Analysis
4.1.2 The LS solution
.................................................................40

4.1.3 Exercises
...........................................................................48

4.2 Properties of LSE
.........................................................................50

4.2.1 Small sample distribution-free properties
.............................51

4.2.2 Properties under normally distributed
errors........................55

4.2.3 Asymptotic properties
........................................................57

4.2.4 Exercises
...........................................................................60

4.3 Estimation under linear restrictions
...............................................60

4.4 Introducing further explanatory variables and related topics
...........67

4.4.1 Introducing further explanatory variables
............................67

4.4.2 Centering and scaling the explanatory variables ...................71

4.4.3 Estimation in terms of linear
prediction...............................72

4.4.4 Exercises
...........................................................................73

4.5 Design matrices of less than full
rank.............................................74

4.5.1 An example
.......................................................................74

4.5.2 Estimability.......................................................................74

4.5.3 Identi.ability under
Constraints..........................................76

4.5.4 Dropping variables to change the model
..............................77

4.5.5 Exercises ...........................................................................77

4.6 Generalized least squares
..............................................................78

4.6.1 Basic theory ......................................................................78

4.6.2 Incorrect speci.cation of variance
matrix.............................80

4.6.3 Exercises
...........................................................................83

4.7 Bayesian
estimation......................................................................83

4.7.1 The basic
idea....................................................................83

4.7.2 Normal-noninformative structure
........................................84

4.7.3 Conjugate priors
................................................................85

4.8 Numerical
examples......................................................................86

4.9
Exercises......................................................................................90

Chapter 5 Testing Linear Hypotheses
..................................................92

5.1 Linear
hypotheses.........................................................................92

5.2 F -Test
.........................................................................................93

5.2.1 F -test................................................................................94

Contents VII
5.2.2 What are actually tested
....................................................95

5.2.3 Examples...........................................................................96

5.3 Con.dence ellipse
....................................................................... 101

5.4 Prediction and calibration...........................................................103

5.5 Multiple correlation coe.cient
.................................................... 105

5.5.1 Variable selection
............................................................. 105

5.5.2 Multiple correlation coe.cient: straight line ......................
106

5.5.3 Multiple correlation coe.cient: multiple regression ............ 108

5.5.4 Partial correlation coe.cient ............................................
110

5.5.5 Adjusted multiple correlation coe.cient ............................
111

5.6 Testing linearity: goodness-of-.t test
........................................... 112

5.7 Multiple
comparisons..................................................................114

5.7.1 Simultaneous inference
..................................................... 114

5.7.2 Some classical methods for simultaneous intervals .............. 116

5.8 Univariate analysis of variance
.................................................... 120

5.8.1 ANOVA
model................................................................. 120

5.8.2 ANCOVA model
.............................................................. 126

5.8.3 SAS procedures for ANOVA
............................................. 127

5.9 Exercises....................................................................................
129

Chapter 6 Variable
Selection............................................................... 133

6.1 Impact of variable selection
......................................................... 133

6.2 Mallows Cp
...............................................................................
137

6.3 Akaikes information criterion
AIC............................................139

6.3.1 Prelimilaries: asymptotic normality of MLE ...................... 140

6.3.2 Kullback-Leiblers distance
............................................... 143

6.3.3 Akaikes Information Criterion ..........................................
144

6.3.4 AIC for linear
regression...................................................147

6.4 Bayesian information criterion BIC
........................................... 150

6.5 Stepwise variable selection
procedures.......................................... 152

6.6 Some newly proposed methods
.................................................... 154

6.6.1 Penalized RSS..................................................................
154

6.6.2 Nonnegative garrote
......................................................... 157

6.7 Final remarks on variable selection
.............................................. 158

Regression Analysis
6.8
Exercises....................................................................................
161

Chapter 7 Miscellaneous for Linear Regression
................................ 165

7.1 Collinearity
................................................................................
165

7.1.1 Introduction
.................................................................... 165

7.1.2 Examine
collinearity......................................................... 166

7.1.3
Remedies.........................................................................169

*7.2 Some remedies for collinearity
..................................................... 170

7.2.1 Ridge
regression...............................................................170

7.2.2 Principal Component Regression
....................................... 173

7.2.3 Partial least square
.......................................................... 175

7.2.4 Exercises
......................................................................... 176

7.3 Outliers .....................................................................................
177

7.3.1 Introduction
.................................................................... 177

7.3.2 Single outlier
................................................................... 179

7.3.3 Multiple outliers
.............................................................. 181

7.3.4 Relevant
quantities........................................................... 183

7.3.5
Remarks..........................................................................185

7.4 Testing features of
errors............................................................. 186

7.4.1 Serial correlation and
Durbin-Watson test ......................... 186

7.4.2 Testing heteroskeasticity and
related topics ....................... 187

7.5 Some extensions and variants
...................................................... 191

7.5.1 Box-Cox model
................................................................ 191

7.5.2 Modeling the variances
..................................................... 192

7.5.3 A
remark.........................................................................193

Chapter 8 Logistic Regression: Modeling Categorical Responses ... 194

8.1 Logistic regression
...................................................................... 194

8.1.1 Logistic regression for
dichotomous responses..................... 194

8.1.2 Likelihood function for
logistic regression........................... 196

8.1.3 Interpreting the logistic
regression.....................................198

8.2 Multiple logistic regression
.......................................................... 199

8.2.1 Maximum likelihood estimation
for multiple logistic regression
........................................................................ 200

Contents IX
8.3 Inference for logistic regression
.................................................... 202

8.3.1 Inference for simple logistic regression
............................... 202

8.3.2 Inference for multiple logistic
regression............................. 204

8.4 Logistic regression for multinomial
responses................................205

8.4.1 Nominal responses baseline-category logistic regression.......206

8.4.2 Ordinal responses: cumulative logistic regression................208

8.5 Exercises....................................................................................
210

Bibliography
............................................................................................
212

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