应用多元统计分析与R软件

PrefaceChapter 1 Introduction1.1 Goal of Statistics1.2 Univariate Analysis1.3 Multivariate Analysis1.4 Multivariate Normal Distribution1.5 Unsupervised Learning and Supervised Learning1.6 Data Analysis Strategies and Statistical Thinking1.7 OutlineExercises 1Chapter 2 Principal Components Analysis2.1 The Basic Idea2.2 The Principal Components2.3 Choose Number of Principal Components2.4 Considerations in Data Analysis2.5 Examples in RExercises 2Chapter 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 4Chapter 5 Inference for a Multivariate Normal Population5.1 Introduction5.2 Inference for Multivariate Means5.3 Inference for Covariance Matrices5.4 Large Sample Inferences about a Population Mean Vector5.5 Examples in RExercises 5Chapter 6 Discrete or Categorical Multivariate Data6.1 Discrete or Categorical Data6.2 The Multinomial Distribution6.3 Contingency Tables6.4 Associations Between Discrete or Categorical Variables6.5 Logit Models for Multinomial Variables6.6 Loglinear Models for Contingency Tables6.7 Example in RExercises 6Chapter 7 Copula Models7.1 Introduction7.2 Copula Models7.3 Measures of Dependence7.4 Applications in Actuary and Finance7.5 Applications in Longitudinal and Survival Data7.6 Example in RExercises 7Chapter 8 Linear and Nonlinear Regression Models8.1 Introduction8.2 Linear Regression Models8.3 Model Selection8.4 Model Diagnostics8.5 Data Analysis Examples with R8.6 Nonlinear Regression Models8.7 More on Model SelectionExercises 8Chapter 9 Generalized Linear Models9.1 Introduction9.2 The Exponential Family9.3 The General Form of a GLM9.4 Inference for GLM9.5 Model Selection and Model Diagnostics9.6 Logistic Regression Models9.7 Poisson Regression ModelsExercises 9Chapter 10 Multivariate Regression and MANOVA Models10.1 Introduction10.2 Multivariate Regression Models10.3 MANOVA Models10.4 Examples in RExercises 10Chapter 11 Longitudinal Data, Panel Data, and Repeated Measurements11.1 Introduction11.2 Methods for Longitudinal Data Analysis11.3 Linear Mixed Effects Models11.4 GEE ModelsExercises 11Chapter 12 Methods for Missing Data12.1 Missing Data Mechanisms12.2 Methods for Missing Data12.3 Multiple Imputation Methods12.4 Multiple Imputation by Chained Equations12.5 The EM Algorithm12.6 Example in RExercises 12Chapter 13 Robust Multivariate Analysis13.1 The Need for Robust Methods13.2 General Robust Methods13.3 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 RExercises 13Chapter 14 Selected Topics14.1 Likelihood Methods14.2 Bootstrap Methods14.3 MCMC Methods and the Gibbs Sampler14.4 Survival Analysis14.5 Data Science, Big Data, and Data MiningReferencesIndex

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 measurements, methods for missing data, robust multivariate analysis, and selected topics. The focus of this book is on conceptual understanding of the models and methods for multivariate data, rather than tedious mathematical derivations or proofs. Extensive real data examples are presented using software R. This book is written as a textbook for undergraduate and graduate students i statistics, as well as graduate students in other fields.