Sparse Precision Matrix Estimation via Vector Half Operator

• Activity Number: 136
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Shota Katayama*+
• Companies: Osaka University
• Keywords: Precision Matrix ; High-Dimensional Data ; Sparse Estimation

Abstract

Estimation of an inverse covariance matrix which is often called precision matrix is a fundamental problem in multivariate analysis. In this talk, we study a method for estimating the sparse precision matrix using the vector half operator. This procedure can be viewed as a linear regression analysis, and hence can be easily implemented. We study theoretical performances of the proposed method under a high-dimensional framework where both the sample size and the dimension tend to infinity. The convergence rates are obtained under the L2 norm and the infinity norm. It is also shown that the proposed estimator can recover the sparse pattern of the precision matrix.