Empirical Likelihood in Nonparametric and Semiparametric: Mathematics Monograph Series 17

This book is composed of ten chapters. The first chapter contains the preliminary knowledge about empirical likelihood and other relevant nonparametric methods. Chapters 2 and 3 analyze the section-data using the single-index model and the partially linear single-index model. Chapters 4 through 6 investigate the longitudinal data using the partially linear model, the varying coefficient model and a nonparametric regression model. Chapter 7 discusses nonlinear errors-in-covariables models with validation data. Chapters 8 through 10 investigate missing data under the framework of the linear model, a nonparametric regression model and the partially linear model. Every chapter, except for Chapter 1, of this book is self-contained so that the reader could focus on any chapter without much effect on the understanding of the others, and hence can read any chapters according to reader's own interest. The emphasis of this book is on methodologies rather than on theory, with a particular focus on applications of the empirical likelihood techniques to various semiparametric regression models. Key technical arguments are presented in the "proofs sections" at the end of each chapter. This gives interested researchers an idea of how the theoretical results are obtained. Also from the style of material organization, this book is more likely a lecture note, rather than a textbook. Most materials come from authors' research articles.
This book intends to provide a useful reference for researchers and to serve as a lecture note to postgraduate students. It is especially for the people working in the nonparametric and semiparametric statistics areas or applying the empirical likelihood method to other areas.

Preface
Chapter 1 Preliminary knowledge
1.1 Empirical likelihood (EL)
1.2 Bootstrap method
1.3 Smoothing methods
1.4 Cross-validation
1.5 Data sets
1.6 Some notations
Chapter 2 EL for single-index models
2.1 Introduction
2.2 Methods and results
2.3 Simulation results
2.4 Proofs
Chapter 3 EL in a partially linear single-index model
3.1 Introduction
3.2 Methodology
3.3 Simulation results
3.4 Proofs
Chapter 4 EL semiparametric regression analysis
4.1 Introduction
4.2 Maximum EL estimator
4.3 Confidence regions for regression coefficients
4.4 Confidence intervals for baseline function
4.5 Numerical results
4.6 Proofs
Chapter 5 EL for a varying coefficient model
5.I Introduction
5.2 Naive EL and maximum EL estimation
5.3 Two bias corrections
5.4 Asymptotic confidence regions
5.5 Numerical results
5.6 Proofs of Theorems
Chapter 6 EL local polynomial regression analysis
6.1 Introduction
6.2 Naive empirical likelihood
6.3 A bias correction method
6.4 Asymptotic confidence regions
6.5 Bandwidth selection
6.6 Numerical results
6.7 Concluding remarks
6.8 Proofs of Theorems
Chapter 7 EL in nonlinear EV models
7.1 Introduction
7.2 Estimated EL
7.3 Adjusted EL
7.4 Simulations and application
7.5 Conclusions
7.6 Proofs
Chapter 8 EL for the linear models
Chapter 9 EL for response mean
Chapter 10 EL for a semiparametric regression model
References
Index