On the theoretic and practical merits of the banding estimator for large covariance matrices, Luo Xiao, Florentina Bunea, 2-2-14

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

Luo Xiao, Florentina Bunea(Submitted on 4 Feb 2014)

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.

Comments: 19 pages, 1 figureSubjects: Statistics Theory (math.ST); Methodology (stat.ME)Cite as: arXiv:1402.0844 [math.ST]  (or arXiv:1402.0844v1 [math.ST] for this version)