Testing covariance structure of large-dimensional data based on Wald’s score test

Abstract

This paper considers testing the covariance matrices structure based on Wald’s score test in large-dimensional setting. The tests for identity and sphericity of large-dimensional covariance matrices are reviewed by the generalized CLT for the linear spectral statistics of large-dimensional sample covariance matrices from [D. D. Jiang, Tests for large-dimensional covariance structure based on Rao’s score test, J. Multivariate Anal. 152 (2016) 28–39]. The proposed test can be applicable for large-dimensional non-Gaussian variables in a wider range. Furthermore, the simulation study is conducted to compare the proposed test with other large-dimensional covariance matrix tests. As seen from the simulation results, our proposed test is feasible for large-dimensional data without restriction of population distribution and provides the accurate and steady empirical sizes, which are almost around the nominal size.