This book intends to examine important issues arising from high-dimensional data analysis to explore key ideas for statistical inference and prediction.It is structured around topics on multiple hypothesis testing, feature selection, regression, classification, dimension reduction, as well as applications in survival analysis and biomedical research.The book will appeal to graduate students and new researchers interested in the plethora of opportunities available in high-dimensional data analysis.

Preface

Part Ⅰ High-Dimensional Classification

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

1 Introduction

2 Elements of classifications

3 Impact of dimensionality on classification

4 Distance-based classification Rules

5 Feature selection by independence rule

6 Loss-based classification

7 Feature selection in loss-based classification

8 Multi-category classification

References

 Chapter 2 Flexible Large Margin Classifiers Yufeng Liu and Yichao Wu

1 Background on classification

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

3 Regularization framework

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

5 Multicategory classifiers

6 Probability estimation

7 Conclusions and discussions

References

Part Ⅱ Large-Scale Multiple Testing

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

1 Introduction

2 FDR controlling procedures based on p-values

3 Oracle and adaptive compound decision rules for FDR control

4 Simultaneous testing of grouped hypotheses

5 Large-scale multiple testing under dependence

6 Open problems

References

Part Ⅲ Model Building with Variable Selection

 Chapter 4 Model Building with Variable Selection Ming Yuan

1 Introduction

2 Why variable selection

3 Classical approaches

4 Bayesian and stochastic search

5 Regularization

6 Towards more interpretable models

7 Further readings

References

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

1 Introduction

2 Statistical models

3 Estimation

4 Results

5 Discussion

References

Part Ⅳ High-Dimensional Statistics in Genomics

 Chapter 6 High-Dimensional Statistics in Genomics Hongzhe Li

1 Introduction

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

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

4 Statistical methods in eQTL studies

5 Discussion and future direction

References

 Chapter 7 An Overview on Joint Modeling of Censored Survival Time and Longitudinal Data

Runze Li and Jian-Jian Ren

1 Introduction

2 Survival data with longitudinal covariates

3 Joint modeling with right censored data

4 Joint modeling with interval censored data

5 Further studies

References

Part Ⅴ Analysis of Survival and Longitudinal Data

 Chapter 8 Survival Analysis with High-Dimensional Covariates Bin Nan

1 Introduction

2 Regularized Cox regression

3 Hierarchically penalized Cox regression with grouped variables ...

4 Regularized methods for the accelerated failure time model

5 Tuning parameter selection and a concluding remark

References

Part Ⅵ  Sufficient Dimension Reduction in Regression

 Chapter 9 Sufficient Dimension Reduction in Regression Xiangrong Yin

1 Introduction

2 Sufficient dimension reduction in regression

3 Sufficient variable selection (SVS)

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

5 Further discussion

References

 Chapter 10 Combining Statistical Procedures Lihua Chen and Yuhong Yang

1 Introduction

2 Combining for adaptation

3 Combining procedures for improvement

4 Concluding remarks

References

Subject Index

Author Index