On weighted U-statistics for stationary processes

• 成果类型: Article
• 署名作者: Hsing, T; Wu, WB
• 署名单位: Texas A&M University System; Texas A&M University College Station; University of Chicago
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117904000000333
• 发表日期: 2004
• 页码: 1600-1631
• 关键词: CENTRAL-LIMIT-THEOREM; bivariate appell polynomials; Empirical Process; asymptotic distributions; BEHAVIOR; functionals; expansion; dimension

摘要

A weighted U-statistic based on a random sample X-1,..., X-n has the form U-n = Sigma(1less than or equal toi, jless than or equal ton) 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.