I. S. Borisov, N. V. Volodko, “Orthogonal series and limit theorems for canonical $U$- and $V$-statistics of stationary connected observations”, Mat. Tr., 11:1 (2008), 25–48; Siberian Adv. Math., 18:4 (2008), 242

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Matematicheskie Trudy, 2008, Volume 11, Number 1, Pages 25–48 (Mi mt115)

This article is cited in 14 scientific papers (total in 14 papers)

Orthogonal series and limit theorems for canonical

$U$ - and

$V$ -statistics of stationary connected observations

I. S. Borisov^ab, N. V. Volodko^ab

^a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
^b Novosibirsk State University

Full-text PDF (264 kB) Citations (14)

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Abstract: The limit behavior is studied for the distributions of normalized

$U$ - and

$V$ -statistics of an arbitrary order with canonical (degenerate) kernels, based on samples of increasing sizes from a stationary sequence of observations satisfying

$\varphi$ -or

$\alpha$ -mixing. The corresponding limit distributions are represented as infinite multilinear forms of a centered Gaussian sequence with a known covariance matrix.

Key words: stationary sequence of random variables, mixing, multiple orthogonal series, canonical

$U$ - and

$V$ -statistics.

Received: 13.09.2007

English version:
Siberian Advances in Mathematics, 2008, Volume 18, Issue 4, Pages 242–257
DOI: https://doi.org/10.3103/S1055134408040020

Bibliographic databases:

UDC: 519.21

Language: Russian

Citation: I. S. Borisov, N. V. Volodko, “Orthogonal series and limit theorems for canonical

$U$ - and

$V$ -statistics of stationary connected observations”, Mat. Tr., 11:1 (2008), 25–48; Siberian Adv. Math., 18:4 (2008), 242–257

Citation in format AMSBIB

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\by I.~S.~Borisov, N.~V.~Volodko

\paper Orthogonal series and limit theorems for canonical $U$- and $V$-statistics of stationary connected observations

\jour Mat. Tr.

\yr 2008

\vol 11

\issue 1

\pages 25--48

\mathnet{http://mi.mathnet.ru/mt115}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2437480}

\transl

\jour Siberian Adv. Math.

\yr 2008

\vol 18

\issue 4

\pages 242--257

\crossref{https://doi.org/10.3103/S1055134408040020}

Linking options:

https://www.mathnet.ru/eng/mt115

https://www.mathnet.ru/eng/mt/v11/i1/p25

This publication is cited in the following 14 articles:

I. S. Borisov, A. A. Bystrov, “Exponential inequalities for the distributions of canonical multiple partial sum processes”, Theory Probab. Appl., 64:2 (2019), 171–185
I. S. Borisov, V. A. Zhechev, “Exponential inequalities for the distributions of $V$ -processes based on dependent observations”, Siberian Adv. Math., 29 (2019), 263–273
I. S. Borisov, N. V. Volod'ko, “Asymptotic expansions for the distributions of canonical $V$ -statistics of third order”, Theory Probab. Appl., 60:1 (2016), 1–18
Borisov I.S. Volodko N.V., “a Note on Exponential Inequalities For the Distribution Tails of Canonical Von Mises' Statistics of Dependent Observations”, Stat. Probab. Lett., 96 (2015), 287–291
Volodko N.V., “Small Deviations of the Determinants of Random Matrices with Gaussian Entries”, Stat. Probab. Lett., 84 (2014), 48–53
Adamczak R., Milos P., “U-Statistics of Ornstein–Uhlenbeck Branching Particle System”, J. Theor. Probab., 27:4 (2014), 1071–1111
Denker M., Gordin M., “Limit Theorems For Von Mises Statistics of a Measure Preserving Transformation”, Probab. Theory Relat. Field, 160:1-2 (2014), 1–45
Leucht A., Neumann M.H., “Degenerate - and -Statistics Under Ergodicity: Asymptotics, Bootstrap and Applications in Statistics”, Ann. Inst. Stat. Math., 65:2 (2013), 349–386
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
Leucht A., Neumann M.H., “Dependent Wild Bootstrap for Degenerate U- and V-Statistics”, J. Multivar. Anal., 117 (2013), 257–280
I. S. Borisov, V. A. Zhechev, “The functional limit theorem for the canonical $U$ -processes defined on dependent trials”, Siberian Math. J., 52:4 (2011), 593–601
I. S. Borisov, D. I. Sidorov, “Limit theorems for additive statistics based on moving average samples”, Siberian Adv. Math., 21:4 (2011), 233–249
N. V. Volod'ko, “Limit theorems for canonical von Mises statistics and $U$ -statistics for $m$ -dependent observations”, Theory Probab. Appl., 55:2 (2011), 271–290
I. S. Borisov, N. V. Volodko, “Exponential inequalities for the distributions of canonical $U$ - and $V$ -statistics of dependent observations”, Siberian Adv. Math., 19:1 (2009), 1–12

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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