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Sibirskii Matematicheskii Zhurnal, 2011, Volume 52, Number 4, Pages 754–764 (Mi smj2236)  
This article is cited in 1 scientific paper (total in 1 paper)

The functional limit theorem for the canonical U-processes defined on dependent trials

I. S. Borisova, V. A. Zhechevb

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
Full-text PDF (299 kB) Citations (1)
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Abstract: The functional limit theorem is proven for a sequence of normalized U-statistics (the socalled U-processes) of arbitrary order with canonical (degenerate) kernels defined on samples of φ-mixing observations of growing size. The corresponding limit distribution is described as that of a polynomial of a sequence of dependent Wiener processes with some known covariance function.
Keywords: canonical U-statistics, invariance principle, stationary sequence of observations, φ-mixing.
Received: 09.02.2011
English version:
Siberian Mathematical Journal, 2011, Volume 52, Issue 4, Pages 593–601
DOI: https://doi.org/10.1134/S0037446611040045
Bibliographic databases:
Document Type: Article
UDC: 519.21
Language: Russian
Citation: I. S. Borisov, V. A. Zhechev, “The functional limit theorem for the canonical U-processes defined on dependent trials”, Sibirsk. Mat. Zh., 52:4 (2011), 754–764; Siberian Math. J., 52:4 (2011), 593–601
Citation in format AMSBIB
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\by I.~S.~Borisov, V.~A.~Zhechev
\paper The functional limit theorem for the canonical $U$-processes defined on dependent trials
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\vol 52
\issue 4
\pages 754--764
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\transl
\jour Siberian Math. J.
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\pages 593--601
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  • https://www.mathnet.ru/eng/smj/v52/i4/p754
    • This publication is cited in the following 1 articles:
    1. I. S. Borisov, V. A. Zhechev, “Invariance principle for canonical U- and V-statistics based on dependent observations”, Siberian Adv. Math., 25:1 (2015), 21–32  mathnet  crossref  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
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