A test for high-dimensional covariance matrices via the extended cross-data-matrix methodology (Statistical Inference and Modelling)

Abstract

In this paper, we consider two-sample tests for covariance matrices in high-dimensional settings. We introduce the extended cross-data-matrix (ECDM) methodology. We construct test statistics by using the ECDM methodology. We show that the ECDM test statistics have the consistency property and the asymptotic normality in high-dimensional settings. We propose a new test procedure based on the ECDM test statistics and evaluate its asymptotic size and power from theoretical and numerical aspects.