Doubly Shrinking of Correlation Matrices

• Activity Number: 136
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 8:30 AM to 10:20 AM
• Sponsor: International Chinese Statistical Association
• Author(s): Sheng-Mao Chang*+
• Companies: National Cheng Kung University
• Keywords: adaptive LASSO ; correlation ; generalized thresholding

Abstract

Correlation matrices play an important role in may multivariate techniques. A good correlation estimation is therefore crucial in this kind of analysis. Sometimes, a correlation matrix is expected to be sparse due to the nature of the data or for the sake of simplification of interpretation. The generalized thresholding estimator possesses good properties such as sparsity, consistency and superior computational efficiency. However, the estimator is not always positive definite especially for not well-conditioned matrices. In this work, we propose a doubly shrinking method which shrinks tiny elements toward zero and then shrinks the correlation matrix toward the identity matrix. The performance of the proposed estimator is explored in terms of relative Frobenius norm. Theory and simulations were deduced under certain correlation matrices with different richness. We conclude that, for estimation, the richness of correlation matrices is the key to the theoretical convergences as well as the finite sample performance.