ASYMPTOTIC NORMALITY FOR EIGENVALUE STATISTICS OF A GENERAL SAMPLE COVARIANCE MATRIX WHEN P/N →∞ AND APPLICATIONS
The asymptotic normality for a large family of eigenvalue statistics of a general sample covariance matrix is derived under the ultra-high dimensional setting, that is, when the dimension to sample size ratio p/n→∞. Based on this CLT result, we extend the covariance matrix test problem to the new ultrahigh 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.
About the Speaker:
Dr Li is currently an associate professor in the Department of Statistics and Data Science, Southern University of Science and Technology. Previously she was a postdoctoral fellow in the Department of Statistics at the Pennsylvania State University. Dr. Li obtained her Ph.D. degree from the Department of Statistics and Actuarial Science at the University of Hong Kong. Dr. Li’s research covers random matrix theory and high dimensional statistics.
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