Random Matrix Theory and Covariance Matrix Estimation

Abstract:

I will give an introduction of modern random matrix theory, in particular the asymptotic theory for eigenvalues of sample covariance matrices. Then I will discuss the high dimensional covariance matrix estimation problem. Using the framework of nonlinear processes described in Wiener (1958), I will talk about the convergence of regularized covariance matrix estimates. These results can be applied to the traditional Wiener-Kolmogorov prediction theory.