**Graduate Studies in Mathematics**

Volume: 119;
2011;
246 pp;
Hardcover

MSC: Primary 62;

Print ISBN: 978-0-8218-5283-5

Product Code: GSM/119

List Price: $67.00

Individual Member Price: $53.60

**Electronic ISBN: 978-1-4704-1593-8
Product Code: GSM/119.E**

List Price: $67.00

Individual Member Price: $53.60

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#### Supplemental Materials

# Mathematical Statistics: Asymptotic Minimax Theory

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*Alexander Korostelev; Olga Korosteleva*

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

# Table of Contents

## Mathematical Statistics: Asymptotic Minimax Theory

- Cover Cover11 free
- Title page iii4 free
- Contents v6 free
- Preface ix10 free
- Part I. Parametric models 112 free
- The Fisher efficiency 314
- The Bayes and minimax estimators 1122
- Asymptotic minimaxity 2132
- Some irregular statistical experiments 4354
- Change-point problem 5162
- Sequential estimators 6576
- Linear parametric regression 8596
- Part II. Nonparametric regression 99110
- Estimation in nonparametric regression 101112
- Local polynomial approximation of regression function 115126
- Estimation of regression in global norms 131142
- Estimation by splines 151162
- Asymptotic optimality in global norms 167178
- Part III. Estimation in nonparametric models 183194
- Estimation of functionals 185196
- Dimension and structure in nonparametric regression 193204
- Adaptive estimation 211222
- Testing of nonparametric hypotheses 227238
- Bibliography 239250
- Index of notation 241252 free
- Index 243254 free
- Back Cover Back Cover1258

#### Readership

Graduate students and research mathematicians interested in mathematical statistics.

#### Reviews

This is a well written book and should be of great interest to advanced graduate students/researchers in mathematical statistics. The material is presented with great clarity by using simple models as opposed to complex ones. ... Overall it should be of great value to advanced graduate students and researchers in theoretical statistics. The book can be recommended for libraries on campuses with a graduate program in statistics.

-- Mathematical Reviews