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Sibirskii Matematicheskii Zhurnal, 2006, Volume 47, Number 6, Pages 1205–1217 (Mi smj929)  
This article is cited in 9 scientific papers (total in 9 papers)

Limit theorems for the canonical von Mises statistics with dependent data

I. S. Borisov, A. A. Bystrov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Full-text PDF (248 kB) Citations (9)
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Abstract: We study the limit behavior of the canonical (i.e., degenerate) von Mises statistics based on samples from a sequence of weakly dependent stationary observations satisfying the $\psi$-mixing condition. The corresponding limit distributions are defined by the multiple stochastic integrals of nonrandom functions with respect to the nonorthogonal Hilbert noises generated by Gaussian processes with nonorthogonal increments.
Keywords: limit theorems, stochastic integral, multiple stochastic integral, elementary stochastic measure, Gaussian processes, stationary sequences of random variables, mixing, $U$- and $V$-statistics.
Received: 03.02.2006
English version:
Siberian Mathematical Journal, 2006, Volume 47, Issue 6, Pages 980–989
DOI: https://doi.org/10.1007/s11202-006-0109-3
Bibliographic databases:
UDC: 519.21
Language: Russian
Citation: I. S. Borisov, A. A. Bystrov, “Limit theorems for the canonical von Mises statistics with dependent data”, Sibirsk. Mat. Zh., 47:6 (2006), 1205–1217; Siberian Math. J., 47:6 (2006), 980–989
Citation in format AMSBIB
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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