Theory of U-Statistics / Edition 1

Theory of U-Statistics / Edition 1

by Vladimir S. Korolyuk, Y.V. Borovskich
     
 

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ISBN-10: 9048143462

ISBN-13: 9789048143467

Pub. Date: 12/01/2010

Publisher: Springer Netherlands

This monograph contains, for the first time, a systematic presentation of the theory of U-statistics. On the one hand, this theory is an extension of summation theory onto classes of dependent (in a special manner) random variables. On the other hand, the theory involves various statistical applications.
The construction of the theory is concentrated around

Overview

This monograph contains, for the first time, a systematic presentation of the theory of U-statistics. On the one hand, this theory is an extension of summation theory onto classes of dependent (in a special manner) random variables. On the other hand, the theory involves various statistical applications.
The construction of the theory is concentrated around the main asymptotic problems, namely, around the law of large numbers, the central limit theorem, the convergence of distributions of U-statistics with degenerate kernels, functional limit theorems, estimates for convergence rates, and asymptotic expansions. Probabilities of large deviations and laws of iterated logarithm are also considered. The connection between the asymptotics of U-statistics destributions and the convergence of distributions in infinite-dimensional spaces are discussed. Various generalizations of U-statistics for dependent multi-sample variables and for varying kernels are examined. When proving limit theorems and inequalities for the moments and characteristic functions the martingale structure of U-statistics and orthogonal decompositions are used. The book has ten chapters and concludes with an extensive reference list.
For researchers and students of probability theory and mathematical statistics.

Product Details

ISBN-13:
9789048143467
Publisher:
Springer Netherlands
Publication date:
12/01/2010
Series:
Mathematics and Its Applications (closed) Series, #273
Edition description:
Softcover reprint of hardcover 1st ed. 1994
Pages:
554
Product dimensions:
6.14(w) x 9.21(h) x 1.15(d)

Table of Contents

Preface. Introduction. 1. Basic Definitions and Notions. 2. General Inequalities. 3. The Law of Large Numbers. 4. Weak Convergence. 5. Functional Limit Theorems. 6. Approximation in Limit Theorems. 7. Asymptotic Expansions. 8. Probabilities of Large Deviations. 9. The Law of Iterated Logarithm. 10. Dependent Variables. Historical and Bibliographical Notes. References. Subject Index.

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