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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2015, Volume 12, Pages 784–794
DOI: https://doi.org/10.17377/semi.2015.12.064 (Mi semr627) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Probability theory and mathematical statistics

On accuracy of approximation in Koul’s theorem for weighted empirical processes

A. I. Sakhanenkoa, O. A. Sukhovershinab

a Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
b Novosibirsk State University, str. Pirogova, 2, 630090, Novosibirsk, Russia
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DOI: https://doi.org/10.17377/semi.2015.12.064
Abstract: Using coupling we obtain an estimate for the distribution of the uniform distance between a given weighted empirical process and an accompanying gaussian process with the same mean and the covariance function. This estimate also allows us to obtain Koul’s theorem under more general sufficient assumptions.
Keywords: weighted empirical processes, gaussian approximation, accuracy of approximation, coupling, accompanying gaussian processes.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-07460-à
03-01-12415-îôè-ì2
Received September 28, 2015, published November 6, 2015
Document Type: Article
UDC: 519.21
MSC: 62G30
Language: Russian
Citation: A. I. Sakhanenko, O. A. Sukhovershina, “On accuracy of approximation in Koul’s theorem for weighted empirical processes”, Sib. Èlektron. Mat. Izv., 12 (2015), 784–794
Citation in format AMSBIB
\Bibitem{SakSuk15}
\by A.~I.~Sakhanenko, O.~A.~Sukhovershina
\paper On accuracy of approximation in Koul’s theorem for weighted empirical processes
\jour Sib. \`Elektron. Mat. Izv.
\yr 2015
\vol 12
\pages 784--794
\mathnet{http://mi.mathnet.ru/semr627}
\crossref{https://doi.org/10.17377/semi.2015.12.064}
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