Nonparametric Estimates of Correlation Matrices via Block Thresholding

• Activity Number: 311
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Linjun Zhang* and Tony Cai
• Companies: University of Pennsylvania and University of Pennsylvania
• Keywords: Adaptive estimation ; block thresholding ; correlation matrix ; spectral norm ; minimax estimation

Abstract

In this paper we consider correlation matrix estimation in a nonparametric fashion. In order to be adaptive to a generalized parameter space, we propose a block thresholding scheme by carefully dividing the correlation matrix. To prove the result to be optimally minimax, we came up with a more friendly version of convergence rate for nonparametric correlation estimation, this proof is relatively short and the inequality is slightly sharper than previous results. In addition, we propose applications to illustrate our idea.