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VOL. 5 | 2009 Limit theorems and exponential inequalities for canonical U- and V-statistics of dependent trials
Igor S. Borisov, Nadezhda V. Volodko

## 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 φ- or α-mixing. The case of m-dependent sequences is separately studied. The corresponding limit distributions are represented as infinite multilinear forms of a centered Gaussian sequence with a known covariance matrix. Moreover, under φ-mixing, exponential inequalities are obtained for the distribution tails of these statistics with bounded kernels.

## Information

Published: 1 January 2009
First available in Project Euclid: 2 February 2010

zbMATH: 1243.60021
MathSciNet: MR2797944

Digital Object Identifier: 10.1214/09-IMSCOLL509

Subjects:
Primary: 60F05 , 60H05
Secondary: 62G20

Keywords: canonical U- and V-statistics , Mixing , multiple orthogonal series , stationary sequence of random variables

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Vol. 5 • 1 January 2009