COVARIANCE AND PRECISION MATRIX ESTIMATION FOR HIGH-DIMENSIONAL TIME SERIES

• 成果类型: Article
• 署名作者: Chen, Xiaohui; Xu, Mengyu; Wu, Wei Biao
• 署名单位: University of Illinois System; University of Illinois Urbana-Champaign; University of Chicago
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/13-AOS1182
• 发表日期: 2013
• 页码: 2994-3021
• 关键词: optimal rates; CONVERGENCE; selection; models

摘要

We consider estimation of covariance matrices and their inverses (a.k.a. precision matrices) for high-dimensional stationary and locally stationary time series. In the latter case the covariance matrices evolve smoothly in time, thus forming a covariance matrix function. Using the functional dependence measure of Wu [Proc. Natl. Acad. Sci. USA 102 (2005) 14150-14154 (electronic)], we obtain the rate of convergence for the thresholded estimate and illustrate how the dependence affects the rate of convergence. Asymptotic properties are also obtained for the precision matrix estimate which is based on the graphical Lasso principle. Our theory substantially generalizes earlier ones by allowing dependence, by allowing nonstationarity and by relaxing the associated moment conditions.