## The Annals of Probability

### On weighted U-statistics for stationary processes

#### Abstract

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

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

Dates
First available in Project Euclid: 18 May 2004

http://projecteuclid.org/euclid.aop/1084884864

Digital Object Identifier
doi:10.1214/009117904000000333

Mathematical Reviews number (MathSciNet)
MR2060311

Zentralblatt MATH identifier
1049.62099

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

#### Citation

Hsing, Tailen; Wu, Wei Biao. On weighted U -statistics for stationary processes. Ann. Probab. 32 (2004), no. 2, 1600--1631. doi:10.1214/009117904000000333. http://projecteuclid.org/euclid.aop/1084884864.

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