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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

Editor(s) Christian Houdré, Vladimir Koltchinskii, David M. Mason, Magda Peligrad

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

Rights: Copyright © 2009, Institute of Mathematical Statistics

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