Tests for large-dimensional covariance structure based on Rao's score test

This paper proposes a new test for covariance matrices based on the correction to Rao's score test in a large-dimension framework. By generalizing the corresponding CLT for linear spectral statistics, the test can be made applicable for large-dimension non-Gaussian variables in a wider range without the 4th-moment restriction. Moreover, the proposed corrected Rao's score test (CRST) remains powerful even when p≫n, which breaks the inherent idea that the corrected tests by RMT can only be used when p