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Teoriya Veroyatnostei i ee Primeneniya, 2001, Volume 46, Issue 4, Pages 724–743
DOI: https://doi.org/10.4213/tvp3797 (Mi tvp3797) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Lyapunov-Type Bounds for $U$-Statistics

I. B. Alberinka, V. Yu. Bentkusb

a University of Nijmegen, Department of Mathematics
b Institute of Mathematics and Informatics
Full-text PDF (1609 kB) Citations (5)
DOI: https://doi.org/10.4213/tvp3797
Abstract: Let $X_1,\dots,X_n$ be independent identically distributed random variables. An optimal Lyapunov (or Berry–Esseen) bound is derived for $U$-statistics of degree 2, that is, statistics of the form $\sum_{j<k}H(X_j,X_k)$, where $H$ is a measurable, symmetric function such that $\mathbf{E}\,|H(X_1,X_2)|<\infty$, assuming that the statistic is nondegenerate.
Keywords: $U$-statistics, Lyapunov-type bound, Berry–Esseen bound, rate of convergence, normal approximations.
Received: 26.01.2000
English version:
Theory of Probability and its Applications, 2002, Volume 46, Issue 4, Pages 571–588
DOI: https://doi.org/10.1137/S0040585X97979299
Bibliographic databases:
Language: English
Citation: I. B. Alberink, V. Yu. Bentkus, “Lyapunov-Type Bounds for $U$-Statistics”, Teor. Veroyatnost. i Primenen., 46:4 (2001), 724–743; Theory Probab. Appl., 46:4 (2002), 571–588
Citation in format AMSBIB
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\jour Theory Probab. Appl.
\yr 2002
\vol 46
\issue 4
\pages 571--588
\crossref{https://doi.org/10.1137/S0040585X97979299}
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  • https://doi.org/10.4213/tvp3797
  • https://www.mathnet.ru/eng/tvp/v46/i4/p724
    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
     
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