Applied Multivariate Statistical Analysis and Related Topics with R

Preface 
Chapter 1 Introduction 
1.1 Goal of Statistics 
1.2 Univariate Analysis 
1.3 Multivariate Analysis 
1.4 Multivariate Normal Distribution 
1.5 Unsupervised Learning and Supervised Learning 
1.6 Data Analysis Strategies and Statistical Thinking 
1.7 Outline 
Exercises 1 

Chapter 2 Principal Components Analysis 
2.1 The Basic Idea 
2.2 The Principal Components 
2.3 Choose Number of Principal Components 
2.4 Considerations in Data Analysis 
2.5 Examples in R 
Exercises 2 

Chapter 3 Factor Analysis 
3.1 The Basic Idea 
3.2 The Factor Analysis Model 
3.3 Methods for Estimation 
3.4 Examples in R 
Exercises 3 

Chapter 4 Discriminant Analysis and Cluster Analysis 
4.1 Introduction 
4.2 Discriminant Analysis 
4.3 Cluster Analysis 
4.4 Examples in R 
Exercises 4 

Chapter 5 Inference for a Multivariate Normal Population 
5.1 Introduction 
5.2 Inference for Multivariate Means 
5.3 Inference for Covariance Matrices 
5.4 Large Sample Inferences about a Population Mean Vector 
5.5 Examples in R 
Exercises 5 

Chapter 6 Discrete or Categorical Multivariate Data 
6.1 Discrete or Categorical Data 
6.2 The Multinomial Distribution 
6.3 Contingency Tables 
6.4 Associations Between Discrete or Categorical Variables 
6.5 Logit Models for Multinomial Variables 
6.6 Loglinear Models for Contingency Tables 
6.7 Example in R 
Exercises 6 

Chapter 7 Copula Models 
7.1 Introduction 
7.2 Copula Models 
7.3 Measures of Dependence 
7.4 Applications in Actuary and Finance 
7.5 Applications in Longitudinal and Survival Data* 
7.6 Example in R 
Exercises 7 

Chapter 8 Linear and Nonlinear Regression Models 
8.1 Introduction 
8.2 Linear Regression Models 
8.3 Model Selection 
8.4 Model Diagnostics 
8.5 Data Analysis Examples with R 
8.6 Nonlinear Regression Models 
8.7 More on Model Selection 
Exercises 8 

Chapter 9 Generalized Linear Models 
9.1 Introduction 
9.2 The Exponential Family 
9.3 The General Form of a GLM 
9.4 Inference for GLM 
9.5 Model Selection and Model Diagnostics 
9.6 Logistic Regression Models 
9.7 Poisson Regression Models 
Exercises 9 

Chapter 10 Multivariate Regression and MANOVA Models 
10.1 Introduction 
10.2 Multivariate Regression Models 
10.3 MANOVA Models 
10.4 Examples in R 
Exercises 10 

Chapter 11 Longitudinal Data， Panel Data， and Repeated Measurements 
11.1 Introduction 
11.2 Methods for Longitudinal Data Analysis 
11.3 Linear Mixed Effects Models 
11.4 GEE Models 
Exercises 11 

Chapter 12 Methods for Missing Data 
12.1 Missing Data Mechanisms 
12.2 Methods for Missing Data 
12.3 Multiple Imputation Methods 
12.4 Multiple Imputation by Chained Equations 
12.5 The EM Algorithm 
12.6 Example in R 
Exercises 12 

Chapter 13 Robust Multivariate Analysis 
13.1 The Need for Robust Methods 
13.2 General Robust Methods 
13.3 Robust Estimates of the Mean and Standard Deviation 
13.4 Robust Estimates of the Covariance Matrix 
13.5 Robust PCA and Regressions 
13.6 Examples in R 
Exercises 13 

Chapter 14 Selected Topics 
14.1 Likelihood Methods 
14.2 Bootstrap Methods 
14.3 MCMC Methods and the Gibbs Sampler 
14.4 Survival Analysis 
14.5 Data Science， Big Data， and Data Mining 
References 
Index