Asymptotic theory of U-statistics

DOI10.1007/BF01056469zbMath0663.62059MaRDI QIDQ1114264

Vladimir S. Korolyuk, Yuri V. Borovskikh

Publication date: 1988

Published in: Ukrainian Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

surveycentral limit theoremU-statisticsasymptotic theoryorthogonal decompositioncanonical decompositionmultiple Wiener integralsreverse martingale structureBerry-Esséen type boundsInequalities for the momentsmartingale structure

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Central limit and other weak theorems (60F05) Nonparametric inference (62G99)

Related Items (5)

\(U\)-statistics in Banach spaces ⋮ Stein's method for nonlinear statistics: a brief survey and recent progress ⋮ Goodness-of-fit tests based on characterization of uniformity by the ratio of order statistics, and their efficiency ⋮ Weighted approximations for Studentized \(U\)-statistics ⋮ U-statistics with conditional kernels for incomplete data models

Cites Work

• Central limit theorem for integrated square error of multivariate nonparametric density estimators
• Invariance principle for symmetric statistics
• Symmetric statistics, Poisson point processes, and multiple Wiener integrals
• Symmetric polynomials of random variables attracted to an infinitely divisible law
• On the weak limits of elementary symmetric polynomials
• Asymptotic distribution of symmetric statistics
• Large sample theory for U-statistics and tests of fit
• A note on asymptotic normality of sums of higher-dimensionally indexed random variables
• Multiple Wiener integral
• Approximation Theorems of Mathematical Statistics
• The asymptotic distributions of incomplete U-statistics
• Central limit theorems for a class of symmetric statistics
• Limiting Behavior of Posterior Distributions when the Model is Incorrect
• An $L^p$-Convergence Theorem
• Splitting a Single State of a Stationary Process into Markovian States
• A Class of Statistics with Asymptotically Normal Distribution
• On the Asymptotic Distribution of Differentiable Statistical Functions
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