Moderate Deviation Principle for the Determinant of Sample Correlation Matrix

Yansong Bai, Yong Zhang, Jingyu Li

Type: Article

Publication Date: 2024-10-23

Citations: 1

DOI: https://doi.org/10.1002/sta4.70009

Abstract

ABSTRACT Let be a sequence of independence random vectors from with population correlation matrix , and its sample correlation matrix is denoted as , where the matrix element represents the Pearson correlation coefficient between the and columns of the data matrix . is an interesting part in multivariate analysis, and the likelihood ratio test (LRT) statistic used to test the complete independence of all components of can be expressed as a function of . On this basis, under the condition that the sample size and the dimension satisfy as , we derive the moderate deviation principle (MDP) of the LRT statistic for the hypothesis testing problem vs .

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