Department Colloquium

Location: CL 435

Speaker: Liqun Wang

Title:  Regularized Estimation of covariance matrix and error variance in high-dimensional models

Abstract:

Estimation of high-dimensional covariance matrix is one of the fundamental and important problems in multivariate analysis and has a wide range of applications in many fields. We present a novel method for sparse covariance matrix estimation via solving a non-convex regularization optimization problem. We establish the asymptotic properties of the proposed estimator and develop a multi-stage convex relaxation method that guarantees any accumulation point of the generated sequence is a first-order stationary point of the non-convex optimization. Moreover, the error bounds of the first two stage estimators of the multi-stage convex relaxation method are derived under some regularity conditions. Numerical results show that our estimator has high degree of sparsity and outperforms the state-of-the-art estimators. We also present a regularized method for estimation of the error variance in high-dimensional linear models.