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

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journal contribution
posted on 2022-07-09, 06:20 authored by Takayuki Yamada

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.


The first author is partially supported by JSPS KAKENHI Grant Number 18K03419 and JSPS KAKENHI Grant Number 21K03371.