- 清华大学出版社
- 9787302446309
- 1-1
- 51000
- 0045178508-3
- 平装
- 16开
- 2016年8月
- 理学
- 数学
- O212.1
- 统计学、数学
- 本科
内容简介
武萍、吴贤毅著的《回归分析(英文版)》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。
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。
目录
Chapter 1 Preliminaries: Matrix Algebra and Random Vectors
1.1 Preliminary matrix algebra
1.1.1 Trace and eigenvalues
1.1.2 Symmetric matrices
1.1.3 Idempotent matrices and orthogonal projection
1.1.4 Singular value decomposition
1.1.5 Vector entiation and generalized inverse
1.1.6 Exercises
1.2 Expectation and covariance
1.2.1 Basic properties
1.2.2 Mean and variance of quadratic forms
1.2.3 Exercises
1.3 Moment generating functions and independence
1.3.1 Exercises
Chapter 2 Multivariate Normal Distributions
2.1 Definitions and fundamental results
2.2 Distribution of quadratic forms
2.3 Exercises
Chapter 3 Linear Regression Models
3.1 Introduction
3.2 Regression interpreted as conditional mean
3.3 Linear regression interpreted as linear prediction
3.4 Some nonlinear regressions
3.5 Typical data structure of linear regression models
3.6 Exercises
Chapter 4 Estimation and Distribution Theory
4.1 Least squares estimation (LSE)
4.1.1 Motivation: why is LS reasonable
Regression
4.1.2 The LS solution
4.1.3 Exercises
4.2 Properties of LSE
4.2.1 Small sample distribution-free properties
4.2.2 Properties under normally distributed errors
4.2.3 Asymptotic properties
4.2.4 Exercises
4.3 Estimation under linear restrictions
4.4 Introducing further explanatory variables and related topics
4.4.1 Introducing further explanatory variables
4.4.2 Centering and scaling the explanatory variables
4.4.3 Estimation in terms of linear prediction.
4.4.4 Exercises
4.5 Design matrices of less than full rank
4.5.1 An example
4.5.2 Estimability
4.5.3 ility under Constraints
4.5.4 Dropping variables to change the model
4.5.5 Exercises
4.6 Generalized least squares
4.6.1 Basic theory
4.6.2 Incorrect specification of variance matrix
4.6.3 Exercises
4.7 Bayesian estimation
4.7.1 The basic idea
4.7.2 Normal-noninformative structure
4.7.3 Conjugate priors
4.8 Numerical examples
4.9 Exercises
Chapter 5 Testing Linear Hypotheses
5.1 Linear hypotheses
5.2 F-Test
5.2.1 F-test
Con
5.2.2 What are actually tested
5.2.3 Examples.
5.3 nce ellipse
5.4 Prediction and calibration
5.5 Multiple correlation coefficient
5.5.1 Variable selection
5.5.2 Multiple correlation coefficient: straight line
5.5.3 Multiple correlation coefficient: multiple regression
5.5.4 Partial correlation coefficient
5.5.5 Adjusted multiple correlation coefficient
5.6 Testing linearity: goodness-of-fit test
5.7 Multiple comparisons
5.7.1 Simultaneous inference
5.7.2 Some classical methods for simultaneous intervals
5.8 Univariate analysis of variance
5.8.1 ANOVA model
5.8.2 ANCOVA model
5.8.3 SAS procedures for ANOVA
5.9 Exercises
Chapter 6 Variable Selection
6.1 Impact of variable selection
6.2 Mallows' Cp
6.3 Akaike's information criterion (AIC)
6.3.1 Prelimilaries: asymptotic normality of MLE
6.3.2 Kullback-Leibler's distance
6.3.3 Akaike's Information Criterion
6.3.4 AIC for linear regression
6.4 Bayesian information criterion (BIC)
6.5 Stepwise variable selection procedures
6.6 Some newly proposed methods
6.6.1 Penalized RSS
6.6.2 Nonnegative garrote
6.7 Final remarks on variable selection
Regression
6.8 Exercises
Chapter 7 Miscellaneous for Linear Regression
7.1 Collinearity
7.1.1 Introduction
7.1.2 Examine collinearity
7.1.3 Remedies
*7.2 Some remedies for collinearity
7.2.1 Ridge regression
7.2.2 Principal Component Regression
7.2.3 Partial least square
7.2.4 Exercises
7.3 Outliers
7.3.1 Introduction
7.3.2 Single outlier
7.3.3 Multiple outliers
7.3.4 Relevant quantities
7.3.5 Remarks
7.4 Testing features of erro
1.1 Preliminary matrix algebra
1.1.1 Trace and eigenvalues
1.1.2 Symmetric matrices
1.1.3 Idempotent matrices and orthogonal projection
1.1.4 Singular value decomposition
1.1.5 Vector entiation and generalized inverse
1.1.6 Exercises
1.2 Expectation and covariance
1.2.1 Basic properties
1.2.2 Mean and variance of quadratic forms
1.2.3 Exercises
1.3 Moment generating functions and independence
1.3.1 Exercises
Chapter 2 Multivariate Normal Distributions
2.1 Definitions and fundamental results
2.2 Distribution of quadratic forms
2.3 Exercises
Chapter 3 Linear Regression Models
3.1 Introduction
3.2 Regression interpreted as conditional mean
3.3 Linear regression interpreted as linear prediction
3.4 Some nonlinear regressions
3.5 Typical data structure of linear regression models
3.6 Exercises
Chapter 4 Estimation and Distribution Theory
4.1 Least squares estimation (LSE)
4.1.1 Motivation: why is LS reasonable
Regression
4.1.2 The LS solution
4.1.3 Exercises
4.2 Properties of LSE
4.2.1 Small sample distribution-free properties
4.2.2 Properties under normally distributed errors
4.2.3 Asymptotic properties
4.2.4 Exercises
4.3 Estimation under linear restrictions
4.4 Introducing further explanatory variables and related topics
4.4.1 Introducing further explanatory variables
4.4.2 Centering and scaling the explanatory variables
4.4.3 Estimation in terms of linear prediction.
4.4.4 Exercises
4.5 Design matrices of less than full rank
4.5.1 An example
4.5.2 Estimability
4.5.3 ility under Constraints
4.5.4 Dropping variables to change the model
4.5.5 Exercises
4.6 Generalized least squares
4.6.1 Basic theory
4.6.2 Incorrect specification of variance matrix
4.6.3 Exercises
4.7 Bayesian estimation
4.7.1 The basic idea
4.7.2 Normal-noninformative structure
4.7.3 Conjugate priors
4.8 Numerical examples
4.9 Exercises
Chapter 5 Testing Linear Hypotheses
5.1 Linear hypotheses
5.2 F-Test
5.2.1 F-test
Con
5.2.2 What are actually tested
5.2.3 Examples.
5.3 nce ellipse
5.4 Prediction and calibration
5.5 Multiple correlation coefficient
5.5.1 Variable selection
5.5.2 Multiple correlation coefficient: straight line
5.5.3 Multiple correlation coefficient: multiple regression
5.5.4 Partial correlation coefficient
5.5.5 Adjusted multiple correlation coefficient
5.6 Testing linearity: goodness-of-fit test
5.7 Multiple comparisons
5.7.1 Simultaneous inference
5.7.2 Some classical methods for simultaneous intervals
5.8 Univariate analysis of variance
5.8.1 ANOVA model
5.8.2 ANCOVA model
5.8.3 SAS procedures for ANOVA
5.9 Exercises
Chapter 6 Variable Selection
6.1 Impact of variable selection
6.2 Mallows' Cp
6.3 Akaike's information criterion (AIC)
6.3.1 Prelimilaries: asymptotic normality of MLE
6.3.2 Kullback-Leibler's distance
6.3.3 Akaike's Information Criterion
6.3.4 AIC for linear regression
6.4 Bayesian information criterion (BIC)
6.5 Stepwise variable selection procedures
6.6 Some newly proposed methods
6.6.1 Penalized RSS
6.6.2 Nonnegative garrote
6.7 Final remarks on variable selection
Regression
6.8 Exercises
Chapter 7 Miscellaneous for Linear Regression
7.1 Collinearity
7.1.1 Introduction
7.1.2 Examine collinearity
7.1.3 Remedies
*7.2 Some remedies for collinearity
7.2.1 Ridge regression
7.2.2 Principal Component Regression
7.2.3 Partial least square
7.2.4 Exercises
7.3 Outliers
7.3.1 Introduction
7.3.2 Single outlier
7.3.3 Multiple outliers
7.3.4 Relevant quantities
7.3.5 Remarks
7.4 Testing features of erro
