High-dimensional Edgeworth expansion of LR statistic for testing block circular symmetry covariance structure and its errors

Gaoming Sun and Junshan Xie

Communications in Statistics - Theory and Methods, 2023, vol. 52, issue 24, 8636-8657

Abstract: The paper considers the asymptotical expansion on the likelihood ratio (LR) statistic for testing the block circular symmetric (BCS) covariance structure of a multivariate Gaussian population. When the number of blocks u and the dimension of each block p satisfy p=p(n)→∞ and pu/(n−1)→c∈(0,1) as the sample size n→∞, the Edgeworth expansion of the null distribution of the LR test statistic and its uniform Berry-Esseen type bound are established. Some numerical simulations indicate that the proposed approximation is more accurate than the traditional Chi-square approximate method on dealing with the high-dimensional test.

Date: 2023
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DOI: 10.1080/03610926.2022.2067877

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