On the invariance principle for U-statistics

DOI10.1016/0304-4149(79)90028-0zbMath0422.62019OpenAlexW1991833270MaRDI QIDQ1133843

Hall, Peter

Publication date: 1979

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0304-4149(79)90028-0

zbMATH Keywords

projectioninvariance principleU-statisticsnondegeneratedegeneratelimit theory

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Nonparametric hypothesis testing (62G10) Asymptotic distribution theory in statistics (62E20)

Related Items

U-Statistics in Sequential Tests and Change Detection, Second Order Stochastic Inclusion, Invariance principles in mathematical statistics, \(L_ p\)-approximations of weighted partial sum processes, A note on invariance principles for v. Mises' statistics, Some nonparametric methods for changepoint problems, Change point tests based on U-statistics with applications in reliability, Invariance principles for changepoint problems, Stein's method for multivariate Brownian approximations of sums under dependence, U-Statistic Based Modified Information Criterion for Change Point Problems, Renewal theory for asymmetric \(U\)-statistics, Percentiles for Cramér-von Mises functionals of Gaussian processes and some applications to Bayesian tests, \(U\)-statistics for change under alternatives, Asymptotic normality for \(U\)-statistics of associated random variables, Asymptotic normality for \(U\)-statistics of negatively associated random variables, Invariance principles for von Mises and U-statistics, Central Limit Theorems for ReducedU-Statistics Under Dependence and Their Usefulness, Central limit theorem for integrated square error of multivariate nonparametric density estimators, Tests for changes under random censorship, Multivariate Kendall's tau for change-point detection in copulas, Functional convergence of sequential \(U\)-processes with size-dependent kernels

Cites Work

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• Functional limit theorems for U-statistics in the degenerate case
• Large sample theory for U-statistics and tests of fit
• Weak convergence of generalized U-statistics
• Asymptotic distributions for quadratic forms with applications to tests of fit
• The Kolmogorov-Smirnov, Cramer-von Mises Tests
• [https://portal.mardi4nfdi.de/wiki/Publication:4092722 Inequalities for max | S k | /b k where k � N r]
• Asymptotic Normality of Simple Linear Rank Statistics Under Alternatives
• Martingale Central Limit Theorems
• A Class of Statistics with Asymptotically Normal Distribution
• Asymptotic Theory of Certain "Goodness of Fit" Criteria Based on Stochastic Processes
• A Test of Goodness of Fit
• The Cramer-Smirnov Test in the Parametric Case