Mathematical Statistics Basic Ideas and Selected Topics, Volume II

INTRODUCTION AND EXAMPLES
Tests of Goodness of Fit and the Brownian Bridge
Testing Goodness of Fit to Parametric Hypotheses
Regular Parameters. Minimum Distance Estimates
Permutation Tests
Estimation of Irregular Parameters
Stein and Empirical Bayes Estimation
Model Selection

TOOLS FOR ASYMPTOTIC ANALYSIS
Weak Convergence in Function Spaces
The Delta Method in Infinite Dimensional Space
Further Expansions

DISTRIBUTION-FREE, UNBIASED, AND EQUIVARIANT PROCEDURES
Introduction
Similarity and Completeness
Invariance, Equivariance, and Minimax Procedures

INFERENCE IN SEMIPARAMETRIC MODELS
Estimation in Semiparametric Models
Asymptotics. Consistency, and Asymptotic Normality
Efficiency in Semiparametric Models
Tests and Empirical Process Theory
Asymptotic Properties of Likelihoods. Contiguity

MONTE CARLO METHODS
The Nature of Monte Carlo Methods
Three Basic Monte Carlo Methods
The Bootstrap
Markov Chain Monte Carlo
Applications of MCMC to Bayesian and Frequentist Inference

NONPARAMETRIC INFERENCE FOR FUNCTIONS OF ONE VARIABLE
Introduction
Convolution Kernel Estimates on R
Minimum Contrast Estimates: Reducing Boundary Bias
Regularization and Nonlinear Density Estimates
Confidence Regions
Nonparametric Regression for One Covariate

PREDICTION AND MACHINE LEARNING
Introduction
Classification and Prediction
Asymptotic Risk Criteria
Oracle Inequalities
Performance and Tuning via Cross Validation
Model Selection and Dimension Reduction
Topics Briefly Touched and Current Frontiers

APPENDIX D: SUPPLEMENTS TO TEXT
APPENDIX E: SOLUTIONS

Problems and Complements appear at the end of each chapter.

Biography

Peter J. Bickel is a professor emeritus in the Department of Statistics and a professor in the Graduate School at the University of California, Berkeley. Dr. Bickel is a member of the American Academy of Arts and Sciences and the National Academy of Sciences. He has been a Guggenheim Fellow and MacArthur Fellow, a recipient of the COPSS Presidents’ Award, and president of the Bernoulli Society and the Institute of Mathematical Statistics. He holds honorary doctorate degrees from the Hebrew University of Jerusalem and ETH Zurich.

Kjell A. Doksum is a senior scientist in the Department of Statistics at the University of Wisconsin–Madison. His research encompasses the estimation of nonparametric regression and correlation curves, inference for global measures of association in semiparametric and nonparametric settings, the estimation of regression quantiles, statistical modeling and analysis of HIV data, the analysis of financial data, and Bayesian nonparametric inference.

" . . . the authors have done a superb job of selecting topics comprising most of the essential knowledge needed formodern research. Furthermore, these modern topics are considered with greater depth and sophistication than is usual in a general purpose text. And throughout its pages the book does a good job of linking the mathematical developments to major examples. The choice of topics and examples, along with the depth of coverage are the most attractive features of this volume."
~RobertW. Keener, University of Michigan