Minimax estimation of covariance and precision matrices for high-dimensional time series with long-memory

被引：2

作者：

Zhang, Qihu ^{[1
]}

Park, Cheolwoo ^{[2
]}

Chung, Jongik ^{[3
]}

机构：

[1] Univ Georgia, Dept Stat, Athens, GA 30602 USA

[2] Korea Adv Inst Sci & Technol, Dept Math Sci, Daejeon, South Korea

[3] Univ Cent Florida, Dept Stat & Data Sci, Orlando, FL 32826 USA

来源：

STATISTICS & PROBABILITY LETTERS | 2021年 / 177卷

基金：

美国国家科学基金会;

关键词：

High-dimensional data; Long-memory; Covariance matrix estimation; Precision matrix estimation; Minimax optimal convergence rates; Matrix norm;

D O I：

10.1016/j.spl.2021.109177

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

This paper concerns the minimax estimation of covariance and precision matrices for high-dimensional time series with long-memory property. We generalize the minimax results for the convergence rates of the estimation of covariance matrices in Shu and Nan (2019) in several directions with a mild assumption, which was mentioned as an open problem in Supplement to Cai and Zhou (2012) for i.i.d. data. We also obtain the minimax results for the convergence rates of the estimation of precision matrices under various norms, which is not considered by Shu and Nan (2019) and Cai and Zhou (2012). (C) 2021 Elsevier B.V. All rights reserved.

引用

页数：6

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