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The main contents of this book include principal components analysis, factor analysis, discriminant analysis and cluster analysis, inference for a multivariate normal population,discrete or categorical multivariate data, copula models, linear and nonlinear regression models, generalized linear models,multivariate regression and MANOVA models, longitudinal data, panel data, and repeated measurementnull
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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
