Variance-corrected tests for covariance structures with high-dimensional data

It has been reported in the literature that the identity and sphericity tests of Chen (2010) suffer from severe size distortion when they are applied to heavy-tailed data. This paper provides a theoretical explanation for this observation. New, variance-corrected identity and sphericity tests are constructed. The proposed tests are simple extensions of the tests due to Chen (2010) but simulation results show that they have much better statistical performance than the latter, and two other existing tests.