# Mathematical Statistics: Asymptotic Minimax Theory

## Book Description

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

## Book Details

- Title: Mathematical Statistics: Asymptotic Minimax Theory
- Author: Alexander Korostelev, Olga Korosteleva
- Length: 246 pages
- Edition: 1
- Language: English
- Publisher: American Mathematical Society
- Publication Date: 2011-02-02
- ISBN-10: 0821852833
- ISBN-13: 9780821852835

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