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Matematicheskie Trudy, 2010, Volume 13, Number 2, Pages 10–32 (Mi mt198)  
Limit theorems for additive statistics based on moving average samples

I. S. Borisovab, D. I. Sidorovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
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Abstract: We study statistics based on samples of moving averages generated by stationary sequence of random variables. The central limit theorem (CLT) is proved for sequences of observations defined by an analytic function of moving averages under consideration. For $U$- and $V$-statistics with canonical (degenerate) kernels, the limit distributions are studied.
Key words: moving averages, central limit theorem, canonical $U$- and $V$-statistics, Hermite polynomials.
Received: 26.04.2010
English version:
Siberian Advances in Mathematics, 2011, Volume 21, Issue 4, Pages 233–249
DOI: https://doi.org/10.3103/S1055134411040018
Bibliographic databases:
Document Type: Article
UDC: 519.21
Language: Russian
Citation: I. S. Borisov, D. I. Sidorov, “Limit theorems for additive statistics based on moving average samples”, Mat. Tr., 13:2 (2010), 10–32; Siberian Adv. Math., 21:4 (2011), 233–249
Citation in format AMSBIB
\Bibitem{BorSid10}
\by I.~S.~Borisov, D.~I.~Sidorov
\paper Limit theorems for additive statistics based on moving average samples
\jour Mat. Tr.
\yr 2010
\vol 13
\issue 2
\pages 10--32
\mathnet{http://mi.mathnet.ru/mt198}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2789955}
\transl
\jour Siberian Adv. Math.
\yr 2011
\vol 21
\issue 4
\pages 233--249
\crossref{https://doi.org/10.3103/S1055134411040018}
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