Block-diagonal test for high-dimensional covariance matrices

Jiayu Lai, Xiaoyi Wang (), Kaige Zhao and Shurong Zheng ()
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Jiayu Lai: Northeast Normal University
Xiaoyi Wang: Beijing Normal University
Kaige Zhao: Northeast Normal University
Shurong Zheng: Northeast Normal University

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2023, vol. 32, issue 1, No 17, 447-466

Abstract: Abstract The structure testing of a high-dimensional covariance matrix plays an important role in financial stock analyses, genetic series analyses, and many other fields. Testing that the covariance matrix is block-diagonal under the high-dimensional setting is the main focus of this paper. Several test procedures that rely on normality assumptions, two-diagonal block assumptions, or sub-block dimensionality assumptions have been proposed to tackle this problem. To relax these assumptions, we develop a test framework based on U-statistics, and the asymptotic distributions of the U-statistics are established under the null and local alternative hypotheses. Moreover, a test approach is developed for alternatives with different sparsity levels. Finally, both a simulation study and real data analysis demonstrate the performance of our proposed methods.

Keywords: Block-diagonal structure; High-dimensional covariance matrix; U-statistic; 62H15; 62E20; 62H10 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11749-022-00842-x

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