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

REFERENCES

INDICES