On weighted U-statistics for stationary processes

2004/10/06 by Tailen Hsing, Wei Biao Wu
Mathematics · #math.PR #msc:60F05 #msc:60G10

paper · pdf · doi:10.1214/009117904000000333

published as Annals of Probability 2004, Vol. 32, No. 2, 1600-1631 · Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/009117904000000333

arxiv created 2004/10/06 · arxiv updated 2009/12/01

Abstract

A weighted U-statistic based on a random sample X₁,...,X_n has the form U_n=∑_{1≤ i,j≤ n}w_i-jK(X_i,X_j), where K is a fixed symmetric measurable function and the w_i are symmetric weights. A large class of statistics can be expressed as weighted U-statistics or variations thereof. This paper establishes the asymptotic normality of U_n when the sample observations come from a nonlinear time series and linear processes.

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