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NOVELIST estimator of large correlation and covariance matrices and their inverses

Huang, Na and Fryzlewicz, Piotr (2018) NOVELIST estimator of large correlation and covariance matrices and their inverses. TEST. ISSN 1133-0686

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Identification Number: 10.1007/s11749-018-0592-4

Abstract

We propose a “NOVEL Integration of the Sample and Thresholded covariance estimators” (NOVELIST) to estimate the large covariance (correlation) and precision matrix. NOVELIST performs shrinkage of the sample covariance (correlation) towards its thresholded version. The sample covariance (correlation) component is non-sparse and can be low-rank in high dimensions. The thresholded sample covariance (correlation) component is sparse, and its addition ensures the stable invertibility of NOVELIST. The benefits of the NOVELIST estimator include simplicity, ease of implementation, computational efficiency and the fact that its application avoids eigenanalysis. We obtain an explicit convergence rate in the operator norm over a large class of covariance (correlation) matrices when the dimension p and the sample size n satisfy log p=n ! 0, and its improved version when p=n ! 0. In empirical comparisons with several popular estimators, the NOVELIST estimator performs well in estimating covariance and precision matrices over a wide range of models and sparsity classes. Real data applications are presented.

Item Type: Article
Official URL: https://link.springer.com/journal/volumesAndIssues...
Additional Information: © 2018 the Authors
Divisions: Statistics
Subjects: H Social Sciences > HA Statistics
Sets: Departments > Statistics
Date Deposited: 04 Jul 2018 11:07
Last Modified: 08 Apr 2019 12:06
Projects: EP/L014246/1
Funders: Engineering and Physical Sciences Research Council
URI: http://eprints.lse.ac.uk/id/eprint/89055

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