A remark on convergence in distribution of \(U\)-statistics

DOI10.1214/aop/1176988850zbMath0801.60015OpenAlexW1969600640MaRDI QIDQ1323284

Joel Zinn, Evarist Giné M.

Publication date: 20 November 1994

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1176988850

zbMATH Keywords

convergence in distribution\(U\)-statistics

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Central limit and other weak theorems (60F05)

Related Items (11)

The LIL for canonical \(U\)-statistics of order 2 ⋮ A universal result in almost sure central limit theory. ⋮ The law of the iterated logarithm and Marcinkiewicz law of large numbers for \(B\)-valued \(U\)-statistics ⋮ Bounds on the tail probability of 𝑈-statistics and quadratic forms ⋮ Functional contour regression ⋮ The LIL for canonical \(U\)-statistics ⋮ The LIL for \(U\)-statistics in Hilbert spaces ⋮ On integrability in the LIL for degenerate \(U\)-statistics ⋮ Characterization of LIL Behavior for Non-DegenerateB-ValuedU-Statistics ⋮ Sub-Bernoulli functions, moment inequalities and strong laws for nonnegative and symmetrized \(U\)-statistics ⋮ Incomplete U -statistics of permanent design

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