Mathematical Statistics: Asymptotic Minimax Theory

This book is designed to bridge the gap between traditional textbooks in statistics and more advanced books that include the sophisticated nonparametric techniques. It covers topics in parametric and nonparametric large-sample estimation theory. The exposition is based on a collection of relatively simple statistical models. It gives a thorough mathematical analysis for each of them with all the rigorous proofs and explanations. The book also includes a number of helpful exercises. Prerequisites for the book include senior undergraduate/beginning graduate-level courses in probability and statistics.

Table of Contents

Part 1 Parametric Models
Chapter 1 The Fisher Efficiency
Chapter 2 The Bayes andMinimax Estimators
Chapter 3 Asymptotic Minimaxity
Chapter 4 Some Irregular Statistical Experiments
Chapter 5 Change-Point Problem
Chapter 6 Sequential Estimators
Chapter 7 Linear Parametric Regression

Part 2 Nonparametric Regression
Chapter 8 Estimation in Nonparametric Regression
Chapter 9 Local Polynomial Approximation of the Regression Function
Chapter 10 Estimation of Regression in Global Norms
Chapter 11 Estimation by Splines
Chapter 12 Asymptotic Optimality in Global Norms

Part 3 Estimation in Nonparametric Models
Chapter 13 Estimation of Functionals
Chapter 14 Dimension and Structure in Non parametric Regression
Chapter 15 Adaptive Estimation
Chapter 16 Testing of Nonparametric Hypotheses