INFERENCE OF WEIGHTED V-STATISTICS FOR NONSTATIONARY TIME SERIES AND ITS APPLICATIONS

• 成果类型: Article
• 署名作者: Zhou, Zhou
• 署名单位: University of Toronto
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/13-AOS1184
• 发表日期: 2014
• 页码: 87-114
• 关键词: CENTRAL-LIMIT-THEOREM; asymptotic-distribution; U-statistics; quadratic-forms; stationary; approximations; distributions; bootstrap; BEHAVIOR

摘要

We investigate the behavior of Fourier transforms for a wide class of nonstationary nonlinear processes. Asymptotic central and noncentral limit theorems are established for a class of nondegenerate and degenerate weighted V-statistics through the angle of Fourier analysis. The established theory for V-statistics provides a unified treatment for many important time and spectral domain problems in the analysis of nonstationary time series, ranging from nonparametric estimation to the inference of periodograms and spectral densities.