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Teoriya Veroyatnostei i ee Primeneniya, 1993, Volume 38, Issue 4, Pages 858–868 (Mi tvp4023)  
Cramér type large deviations for some $U$-statistics

T. Inglot, T. Ledwinaa

a Institute of Mathematics, Technical University of Wroclaw, Wroclaw, Poland
Full-text PDF (572 kB)
Abstract: We prove Cramér type large deviations for some $U$-statistics of degree two with kernel $h(x,y)$ being of bounded variation on bounded rectangles. The proof consists of two basic steps. First some explicit bounds (similar to Helmers' bounds for $L$-statistics) for the $U$-statistics are obtained. Then Linnik's result and some results exploiting strong approximations are applied.
Keywords: $U$-statistics, large deviations, strong approximations.
Received: 26.06.1990
English version:
Theory of Probability and its Applications, 1993, Volume 38, Issue 4, Pages 651–659
DOI: https://doi.org/10.1137/1138065
Bibliographic databases:
Language: English
Citation: T. Inglot, T. Ledwina, “Cramér type large deviations for some $U$-statistics”, Teor. Veroyatnost. i Primenen., 38:4 (1993), 858–868; Theory Probab. Appl., 38:4 (1993), 651–659
Citation in format AMSBIB
\Bibitem{IngLed93}
\by T.~Inglot, T.~Ledwina
\paper Cram\'er type large deviations for some $U$-statistics
\jour Teor. Veroyatnost. i Primenen.
\yr 1993
\vol 38
\issue 4
\pages 858--868
\mathnet{http://mi.mathnet.ru/tvp4023}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1318002}
\zmath{https://zbmath.org/?q=an:0834.60030}
\transl
\jour Theory Probab. Appl.
\yr 1993
\vol 38
\issue 4
\pages 651--659
\crossref{https://doi.org/10.1137/1138065}
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