Estimation for almost periodic processes

• 成果类型: Article
• 署名作者: Lii, Keh-Shin; Rosenblatt, Murray
• 署名单位: University of California System; University of California Riverside; University of California System; University of California San Diego
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000000218
• 发表日期: 2006
• 页码: 1115-1139
• 关键词: correlated processes; time-series

摘要

Processes with almost periodic covariance functions have spectral mass on lines parallel to the diagonal in the two-dimensional spectral plane. Methods have been given for estimation of spectral mass on the lines of spectral concentration if the locations of the lines are known. Here methods for estimating the intercepts of the lines of spectral concentration in the Gaussian case are given under appropriate conditions. The methods determine rates of convergence sufficiently fast as the sample size n -> infinity so that the spectral estimation on the estimated lines can then proceed effectively. This task involves bounding the maximum of an interesting class of non-Gaussian possibly nonstationary processes.