The Annals of Probability

On weighted U-statistics for stationary processes

Tailen Hsing and Wei Biao Wu

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A weighted U-statistic based on a random sample X1,,Xn has the form Un=1i,jnwijK(Xi,Xj), where K is a fixed symmetric measurable function and the wi 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 Un when the sample observations come from a nonlinear time series and linear processes.

Article information

Ann. Probab., Volume 32, Number 2 (2004), 1600-1631.

First available in Project Euclid: 18 May 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems
Secondary: 60G10: Stationary processes

Limit theorem nonlinear time series U-statistics linear processes


Hsing, Tailen; Wu, Wei Biao. On weighted U -statistics for stationary processes. Ann. Probab. 32 (2004), no. 2, 1600--1631. doi:10.1214/009117904000000333.

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