Moderate Deviation Principle for the Determinant of Sample Correlation Matrix

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 .