ESTIMATION OF LARGE COVARIANCE AND PRECISION MATRICES FROM TEMPORALLY DEPENDENT OBSERVATIONS

• 成果类型: Article
• 署名作者: Shu, Hai; Nan, Bin
• 署名单位: University of Michigan System; University of Michigan; University of California System; University of California Irvine
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/18-AOS1716
• 发表日期: 2019
• 页码: 1321-1350
• 关键词: functional connectivity; Optimal Rates; regularized estimation; model-selection; CONVERGENCE; STABILITY

摘要

We consider the estimation of large covariance and precision matrices from high-dimensional sub-Gaussian or heavier-tailed observations with slowly decaying temporal dependence. The temporal dependence is allowed to be long-range so with longer memory than those considered in the current literature. We show that several commonly used methods for independent observations can be applied to the temporally dependent data. In particular, the rates of convergence are obtained for the generalized thresholding estimation of covariance and correlation matrices, and for the constrained l(1) minimization and the l(1) penalized likelihood estimation of precision matrix. Properties of sparsistency and sign-consistency are also established. A gap-block cross-validation method is proposed for the tuning parameter selection, which performs well in simulations. As a motivating example, we study the brain functional connectivity using resting-state fMRI time series data with long-range temporal dependence.