U-statistics are universal objects of modern probabilisticsummation theory. They appear in various statistical problems and havevery important applications. The mathematical nature of this class ofrandom variables has a functional character and, therefore, leads to theinvestigation of probabilistic distributions in infinite-dimensionalspaces. The situation when the kernel of a U-statistic takes values ina Banach space, turns out to be the most natural and interesting.
In this book, the author presents in a systematic form the probabilistictheory of U-statistics with values in Banach spaces (UB-statistics),which has been developed to date. The exposition of the material in thisbook is based around the following topics:
algebraic and martingale properties of U-statistics; inequalities; lawof large numbers; the central limit theorem; weak convergence to aGaussian chaos and multiple stochastic integrals; invariance principleand functional limit theorems; estimates of the rate of weakconvergence; asymptotic expansion of distributions; large deviations;law of iterated logarithm; dependent variables; relation betweenBanach-valued U-statistics and functionals from permanent randommeasures.
This book will be of value and interest to researchers working in thefields of statistics and probablity.
1996; xii+420 pages ISBN 90-6764-200-2 Price (all prices are subject to change without notice): EUR 230/US$ 329
