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On weighted U-statistics for stationary processes

Tailen Hsing·Wei Biao Wu
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Abstract

A weighted U-statistic based on a random sample X_1,...,X_n has the form U_n=\sum_{1\le i,j\le n}w_{i-j}K(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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Tailen Hsing, Wei Biao Wu. 2004-10-06. On weighted U-statistics for stationary processes. https://doi.org/10.1214/009117904000000333

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