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Cover Art
E-RESOURCE
Author Koroljuk, V. S.

Title Theory of U-Statistics [electronic resource] / by V.S. Koroljuk, Yu. V. Borovskich.

Published Dordrecht : Springer Netherlands, 1994.

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 UniM INTERNET resource    AVAILABLE
Physical description 1 online resource (ix, 554 pages).
Series Mathematics and Its Applications ; 273
Mathematics and Its Applications ; 273.
Summary 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.
Other author Borovskikh, 뉬U. V. (뉬Uri橠Vasil嶩ch)
Subject Statistics.
Statistics.
Electronic books.
ISBN 9789401735155 (electronic bk.)
9401735158 (electronic bk.)
9789048143467
9048143462
9401735158