Sure-Assisted Tapering Estimation of Large Covariance Matrices

• Activity Number: 136
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Feng Yi*+ and Hui Zou
• Companies: University of Minnesota and University of Minnesota
• Keywords: covariance matrix estimation ; high-dimensional data ; Frobenius norm ; tapering estimation

Abstract

A recent paper by Cai, Zhang and Zhou (2009) revealed the optimal minimax rates of convergence for high-dimensional covariance matrix estimation. Cai, Zhang and Zhou further proved that the tapering estimator can achieve the optimal rate if the tapering parameter is chosen according to the unknown sparse index parameter and the matrix norm. In order to apply the tapering estimator in practice, it is critically important to have a data-driven method to select the optimal tapering parameter. In this work we use Stein's unbiased risk estimation (SURE) to select the tapering parameter under the Frobenius norm. We show that with high probability SURE selects the optimal tapering parameter for the Frobenius norm without using the unknown sparse index parameter. For the matrix L_1 and L_2 norms, the SURE selected tapering parameter can be used to compute the optimal L_1 and L_2 tapering parameters. We conduct extensive simulation study to demonstrate the good performance of SURE-assisted Tapering estimator.