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Part Ⅰ High-Dimensional Classification 3

Chapter 1 High-Dimensional Classification&Jianqing Fan,Yingying Fan and Yichao Wu 3

1 Introduction 3

2 Elements of classifications 4

3 Impact of dimensionality on classification 8

4 Distance-based classification Rules 14

5 Feature selection by independence rule 20

6 Loss-based classification 24

7 Feature selection in loss-based classification 27

8 Multi-category classification 31

References 34

Chapter 2 Flexible Large Margin Classifiers&Yufeng Liu and Yichao Wu 39

1 Background on classification 39

2 The support vector machine:the margin formulation and the SV interpretation 40

3 Regularization framework 45

4 Some extensions of the SVM:Bounded constraint machine and the balancing SVM 48

5 Multicategory classifiers 51

6 Probability estimation 62

7 Conclusions and discussions 66

References 67

Part Ⅱ Large-Scale Multiple Testing 75

Chapter 3 A Compound Decision-Theoretic Approach to Large-Scale Multiple Testing&T Tony Cai and Wenguang Sun 75

1 Introduction 75

2 FDR controlling procedures based on p-values 79

3 Oracle and adaptive compound decision rules for FDR control 82

4 Simultaneous testing of grouped hypotheses 93

5 Large-scale multiple testing under dependence 102

6 Open problems 111

References 112

Part Ⅲ Model Building with Variable Selection 119

Chapter 4 Model Building with Variable Selection&Ming Yuan 119

1 Introduction 119

2 Why variable selection 120

3 Classical approaches 121

4 Bayesian and stochastic search 125

5 Regularization 128

6 Towards more interpretable models 134

7 Further readings 141

References 142

Chapter 5 Bayesian Variable Selection in Regression with Networked Predictors&Feng Tai,Wei Pan and Xiaotong Shen 147

1 Introduction 147

2 Statistical models 149

3 Estimation 152

4 Results 154

5 Discussion 162

References 163

Part Ⅳ High-Dimensional Statistics in Genomics 169

Chapter 6 High-Dimensional Statistics in Genomics&Hongzhe Li 169

1 Introduction 169

2 Identification of active transcription factors using time-course gene expression data 173

3 Methods for analysis of genomic data with a graphical structure 178

4 Statistical methods in eQTL studies 182

5 Discussion and future direction 187

References 188

Chapter 7 An Overview on Joint Modeling of Censored Survival Time and Longitudinal Data&Runze Li and Jian-Jian Ren 195

1 Introduction 195

Chapter 9 Sufficient Dimension Reduction in Regression&Xiangrong Yin 257

1 Instroduction 257

2 Sufficient Dimension reduction in regression 258

3 Sufficient variable selection(SVS) 265

4 SDR for correlated data and large-p-small-n 266

5 Further discussion 267

Chapter 10 Combining Statistical Procedures&Lihua Chen and Yuhong Yang 275

1 Introduction 275

2 Combining for adaptation 279

3 Combining procedures for improvement 288

4 Concluding remarks 294

References 295

Subject Index 299

Author Index 301