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
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.
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页数:13
相关论文
共 23 条
  • [1] Recent advances in functional data analysis and high-dimensional statistics
    Aneiros, German
    Cao, Ricardo
    Fraiman, Ricardo
    Genest, Christian
    Vieu, Philippe
    [J]. JOURNAL OF MULTIVARIATE ANALYSIS, 2019, 170 : 3 - 9
  • [2] Detecting positive correlations in a multivariate sample
    Arias-Castro, Ery
    Bubeck, Sebastien
    Lugosi, Gabor
    [J]. BERNOULLI, 2015, 21 (01) : 209 - 241
  • [3] DETECTION OF CORRELATIONS
    Arias-Castro, Ery
    Bubeck, Sebastien
    Lugosi, Gabor
    [J]. ANNALS OF STATISTICS, 2012, 40 (01) : 412 - 435
  • [4] Bellec P.C, 2019, ARXIV E PRINTS
  • [5] Bettache N., 2022, J MULTIVARIATE ANAL, DOI [10.1016/j.jmva.2021.10, DOI 10.1016/J.JMVA.2021.104883]
  • [6] Sharp minimax tests for large covariance matrices and adaptation
    Butucea, Cristina
    Zgheib, Rania
    [J]. ELECTRONIC JOURNAL OF STATISTICS, 2016, 10 (02): : 1927 - 1972
  • [7] Sharp minimax tests for large Toeplitz covariance matrices with repeated observations
    Butucea, Cristina
    Zgheib, Rania
    [J]. JOURNAL OF MULTIVARIATE ANALYSIS, 2016, 146 : 164 - 176
  • [8] Detection of a sparse submatrix of a high-dimensional noisy matrix
    Butucea, Cristina
    Ingster, Yuri I.
    [J]. BERNOULLI, 2013, 19 (5B) : 2652 - 2688
  • [9] Optimal hypothesis testing for high dimensional covariance matrices
    Cai, T. Tony
    Ma, Zongming
    [J]. BERNOULLI, 2013, 19 (5B) : 2359 - 2388
  • [10] Two-Sample Covariance Matrix Testing and Support Recovery in High-Dimensional and Sparse Settings
    Cai, Tony
    Liu, Weidong
    Xia, Yin
    [J]. JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 2013, 108 (501) : 265 - 277