ASYMPTOTIC NORMALITY FOR EIGENVALUE STATISTICS OF A GENERAL SAMPLE COVARIANCE MATRIX WHEN p/n? 8 AND APPLICATIONS

The asymptotic normality for a large family of eigenvalue statistics of a general sample covariance matrix is derived under the ultrahigh-dimensional setting, that is, when the dimension to sample size ratio p/n & RARR; & INFIN;. Based on this CLT result, we extend the covariance matrix test problem to the new ultra-high-dimensional context, and apply it to test a matrix-valued white noise. Simulation experiments are conducted for the investigation of finite-sample properties of the general asymptotic normality of eigenvalue statistics, as well as the two developed tests.

Automated summary

The paper derives the asymptotic normality for a large family of eigenvalue statistics of a general sample covariance matrix under the ultrahigh-dimensional setting. Based on this result, the covariance matrix test problem is extended to the new ultra-high-dimensional context and applied to test a matrix-valued white noise. Simulation experiments are conducted to investigate the finite-sample properties of the general asymptotic normality of eigenvalue statistics and the two developed tests.