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Contents
Preface
Chapter 1 Introduction 1
1.1 Goal of Statistics 1
1.2 Univariate Analysis 3
1.3 Multivariate Analysis 7
1.4 Multivariate Normal Distribution 16
1.5 Unsupervised Learning and Supervised Learning 21
1.6 Data Analysis Strategies and Statistical Thinking 23
1.7 Outline 26
Exercises 1 27
Chapter 2 Principal Components Analysis 29
2.1 The Basic Idea 29
2.2 The Principal Components 30
2.3 Choose Number of Principal Components 34
2.4 Considerations in Data Analysis 35
2.5 Examples in R 37
Exercises 2 43
Chapter 3 Factor Analysis 45
3.1 The Basic Idea 45
3.2 The Factor Analysis Model 46
3.3 Methods for Estimation 47
3.4 Examples in R 50
Exercises 3 54
Chapter 4 Discriminant Analysis and Cluster Analysis 56
4.1 Introduction 56
4.2 Discriminant Analysis 57
4.3 Cluster Analysis 61
4.4 Examples in R 64
Exercises 4 69
Chapter 5 Inference for a Multivariate Normal Population 71
5.1 Introduction 71
5.2 Inference for Multivariate Means 72
5.3 Inference for Covariance Matrices 75
5.4 Large Sample Inferences about a Population Mean Vector 76
5.5 Examples in R 76
Exercises 5 79
Chapter 6 Discrete or Categorical Multivariate Data 80
6.1 Discrete or Categorical Data 80
6.2 The Multinomial Distribution 81
6.3 Contingency Tables 83
6.4 Associations Between Discrete or Categorical Variables 85
6.5 Logit Models for Multinomial Variables 87
6.6 Loglinear Models for Contingency Tables 89
6.7 Example in R 91
Exercises 6 95
Chapter 7 Copula Models 97
7.1 Introduction 97
7.2 Copula Models 99
7.3 Measures of Dependence 102
7.4 Applications in Actuary and Finance 103
7.5 Applications in Longitudinal and Survival Data£¿ 106
7.6 Example in R 107
Exercises 7 110
Chapter 8 Linear and Nonlinear Regression Models 111
8.1 Introduction 111
8.2 Linear Regression Models 112
8.3 Model Selection 114
8.4 Model Diagnostics 116
8.5 Data Analysis Examples with R 117
8.6 Nonlinear Regression Models 122
8.7 More on Model Selection 125
Exercises 8 129
Chapter 9 Generalized Linear Models 131
9.1 Introduction 131
9.2 The Exponential Family 132
9.3 The General Form of a GLM 133
9.4 Inference for GLM 135
9.5 Model Selection and Model Diagnostics 137
9.6 Logistic Regression Models 140
9.7 Poisson Regression Models 146
Exercises 9 149
Chapter 10 Multivariate Regression and MANOVA Models 152
10.1 Introduction 152
10.2 Multivariate Regression Models 153
10.3 MANOVA Models 156
10.4 Examples in R 157
Exercises 10 162
Chapter 11 Longitudinal Data£¬ Panel Data£¬ and Repeated
Measurements 164
11.1 Introduction 164
11.2 Methods for Longitudinal Data Analysis 165
11.3 Linear Mixed Effects Models 167
11.4 GEE Models 171
Exercises 11 174
Chapter 12 Methods for Missing Data 175
12.1 Missing Data Mechanisms 175
12.2 Methods for Missing Data 178
12.3 Multiple Imputation Methods 181
12.4 Multiple Imputation by Chained Equations 183
12.5 The EM Algorithm 184
12.6 Example in R 187
Exercises 12 192
Chapter 13 Robust Multivariate Analysis 193
13.1 The Need for Robust Methods 193
13.2 General Robust Methods 195
13.3 Robust Estimates of the Mean and Standard Deviation 199
13.4 Robust Estimates of the Covariance Matrix 201
13.5 Robust PCA and Regressions 203
13.6 Examples in R 205
Exercises 13 210
Chapter 14 Selected Topics 211
14.1 Likelihood Methods 211
14.2 Bootstrap Methods 214
14.3 MCMC Methods and the Gibbs Sampler 215
14.4 Survival Analysis 217
14.5 Data Science£¬ Big Data£¬ and Data Mining 220
References 224
Index 225