This article is cited 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<sup>ab

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

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.

UDC: 519.21

Received: 13.09.2007

 English version: Siberian Advances in Mathematics, 2008, 18:4, 242–257

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