Fast nonasymptotic testing and support recovery for large sparse Toeplitz covariance matrices

被引：0

作者：

Bettache, Nayel ^{[1
]}

Butucea, Cristina ^{[1
]}

Sorba, Marianne ^{[1
]}

机构：

[1] CREST, ENSAE Paris, 5 Ave Le Chatelier, F-91120 Palaiseau, France

来源：

JOURNAL OF MULTIVARIATE ANALYSIS | 2022年 / 190卷

关键词：

Covariance matrix; High-dimensional vectors; Hypothesis testing; Sparsity; Support recovery; Time series; SHARP MINIMAX TESTS;

D O I：

10.1016/j.jmva.2021.104883

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：

We consider n independent p-dimensional Gaussian vectors with covariance matrix having Toeplitz structure. The aim is two-fold: to test that these vectors have independent components against a stationary distribution with sparse Toeplitz covariance matrix, and also to select the support of non-zero entries under the alternative hypothesis. Our model assumes that the non-zero values occur in the recent past (time-lag less than p/2). We build test procedures that combine a sum and a scan-type procedure, but are computationally fast, and show their non-asymptotic behaviour in both one-sided (only positive correlations) and two-sided alternatives, respectively. We also exhibit a selector of significant lags and bound the Hamming-loss risk of the estimated support. These results can be extended to the case of nearly Toeplitz covariance structure and to sub-Gaussian vectors. Numerical results illustrate the excellent behaviour of both test procedures and support selectors - larger the dimension p, faster are the rates. (c) 2021 Elsevier Inc. All rights reserved.

引用

页数：13