V. S. Koroli͡uk, Vladimir S. Korolyuk, Y.V. Borovskich

Theory of U-statistics

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Author

Contributions

Borovskikh, I͡U. V. - Contributor

Publication

1994 - Kluwer Academic Publishers, Dordrecht, Netherlands

Language

English

Word Count

138,000 words, Guess

Page Count

552 pages

Identifiers

ISBN-100792326083
ISBN-139780792326083
Library of Congress Control Number94119398
Better World Books9780792326083
Open LibraryOL1147135M

Classifications

DDC519.5/2
LCCQA276.7 .K6713 1994
LCCQA276-280

Description

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.