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Activity Number: 559
Type: Contributed
Date/Time: Wednesday, August 6, 2014 : 2:00 PM to 3:50 PM
Sponsor: International Chinese Statistical Association
Abstract #311488 View Presentation
Title: Sure Based Banding/Tapering Parameter Choice for the Regularized Estimation of Large Covariance Matrices
Author(s): Danning Li*+ and Hui Zou
Companies: and University of Minnesota
Keywords: Frobenius risk ; Regularized estimator ; Consistency ; Covariance matrix ; SURE ; High dimension
Abstract:

Bandable covariance matrices are often used to model the dependence structure of variables that follow a natural order. The banding/tapering estimator gives a good estimation of such bandable covariance matrices in high dimensional case. The choice of the banding/tapering parameter influences the estimation risk significantly. In this paper, we develop a generalized Stein's Unbiased Risk Estimation (GSURE) to estimate the generalized Frobenius risk of the banding/tapering estimator. We establish the limiting distribution and concentration inequality of the GSURE formula. These asymptotic results lead to a tuning procedure to determine a good banding/tapering parameter. We also show that the chosen banding/tapering parameter is equal to the true one almost surely under certain circumstance. Simulations are used to demonstrate the performance of this new tuning method.


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