On the theoretic and practical merits of the banding estimator for large covariance matrices

Abstract

This paper considers the banding estimator proposed in Bickel and Levina (2008) for estimation of large covariance matrices. We prove that the banding estimator achieves rate-optimality under the operator norm, for a class of approximately banded covariance matrices, improving the existing results in Bickel and Levina (2008). In addition, we propose a Stein's unbiased risk estimate (Sure)-type approach for selecting the bandwidth for the banding estimator. Simulations indicate that the Sure-tuned banding estimator outperforms competing estimators.

19 pages, 1 figure

References in corpus (3)

• Adaptive covariance matrix estimation through block thresholding
• The asymptotic distribution and Berry--Esseen bound of a new test for independence in high dimension with an application to stochastic optimization
• Test for bandedness of high-dimensional covariance matrices and bandwidth estimation

Cited by in corpus (2)

• Convex Banding of the Covariance Matrix
• Minimax Estimation of Large Precision Matrices with Bandable Cholesky Factor