High-dimensional asymptotic expansion of the null distribution for Schott’s test statistic for complete independence of normal random variables

Takayuki Yamada

Communications in Statistics - Theory and Methods, 2024, vol. 53, issue 3, 909-925

Abstract: This article is concerned with the testing complete independence for the elements of observed vector. Schott proposed the testing statistic T and gave limiting null distribution under the high-dimensional asymptotic framework that the sample size n and the dimensionality p go to infinity together while p/n converges to a positive constant. In this article we give a one-term asymptotic expansion of the null distribution for T as min{n,p} tends toward infinity. We derive a correction of the critical point for Schott’s test based on this expansion. The finite sample size and dimensionality performance for attained significance level is evaluated in a simulation study and the results are compared to those of Schott’s test.

Date: 2024
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DOI: 10.1080/03610926.2022.2094414

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