Glivenko-Cantelli properties of some generalized empirical DF's and strong convergence of generalized L-statistics

DOI10.1007/BF00319105zbMath0631.60032OpenAlexW2080600395MaRDI QIDQ1094746

Roelof Helmers, Paul Janssen, Robert J. Serfling

Publication date: 1988

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00319105

zbMATH Keywords

U-statistics almost sure convergence generalized L-statistics exponential probability inequalities L-statistics generalized empirical distributions generalized form of L-functional Glivenko-Cantelli convergence properties U- statistic

Mathematics Subject Classification ID

Order statistics; empirical distribution functions (62G30) Strong limit theorems (60F15)

Related Items

New tests for exponentiality based on a characterization with random shift, $U$-processes indexed by Vapnik-Červonenkis classes of functions with applications to asymptotics and bootstrap of $U$-statistics with estimated parameters, Weak and strong representations for trimmed U-statistics, Distribution-free goodness-of-fit tests for the Pareto distribution based on a characterization, Glivenko-Cantelli properties of some generalized empirical DF's and strong convergence of generalized L-statistics, Asymptotic efficiency of new exponentiality tests based on a characterization, Goodness-of-fit tests for the Pareto distribution based on its characterization, Characterization based symmetry tests and their asymptotic efficiencies, Strong laws for generalized absolute Lorenz curves when data are stationary and ergodic sequences, Asymptotic normality of generalized L-statistics with unbounded scores, Tests of exponentiality based on Arnold-Villasenor characterization and their efficiencies, Local exact Bahadur efficiencies of two scale-free tests of normality based on a recent characterization, Goodness-of-fit tests based on characterization of uniformity by the ratio of order statistics, and their efficiency, Exponentiality tests based on Ahsanullah's characterization and their efficiency, Comparison of efficiencies of some symmetry tests around an unknown centre, Limit theorems for functionals of mixing processes with applications to $U$-statistics and dimension estimation, Kolmogorov tests of normality based on some variants of Polya's characterization, Asymptotic efficiency of new distribution-free tests of symmetry for generalized skew alternatives, Berry-Esseen type bounds for trimmed $U$-statistics, New Versions of Some Classical Stochastic Inequalities, Multivariate spatial U-quantiles: A Bahadur-Kiefer representation, a Theil-Sen estimator for multiple regression, and a robust dispersion estimator, Non-Gaussian limit distributions forU-statistics based on trimmed and Winsorized samples, Large deviations of U-empirical Kolmogorov–Smirnov tests and their efficiency, The law of the iterated logarithm and central limit theorem for $L$-statistics, Alternative empirical distributions based on weighted linear combinations of order statistics, Efficiency of exponentiality tests based on a special property of exponential distribution, Toward the history of the St. Petersburg school of probability and statistics. IV: Characterization of distributions and limit theorems in statistics, Two-dimensional Kolmogorov-type goodness-of-fit tests based on characterisations and their asymptotic efficiencies, Moderate and large deviations for $U$-processes, ESTIMATING THE ASYMPTOTIC VARIANCE OF GENERALIZEDL-STATISTICS, New characterization-based symmetry tests, The Bahadur-Kiefer representation for $U$-quantiles, Weak convergence and Glivenko-Cantelli results for empirical processes of U-statistic structure, A Correlation Test for Normality Based on the Lévy Characterization, Goodness-of-fit tests for the logistic location family, Jackknife variance estimators for generalized L-statistics

Cites Work