Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

Abstract

This paper considers ridge-type shrinkage estimation of a large dimensional precision matrix. The asymptotic optimal shrinkage coefficients and the theoretical loss are derived. Data-driven estimators for the shrinkage coefficients are also conducted based on the asymptotic results from random matrix theory. The new method is distribution-free and no assumption on the structure of the covariance matrix or the precision matrix is required. The proposed method also applies to situations where the dimension is larger than the sample size. Numerical studies of simulated and real data demonstrate that the proposed estimator performs better than existing competitors in a wide range of settings.

Keywords

Large dimensional data, Precision matrix, Random matrix theory, Ridge-type estimator, Shrinkage estimation

Publication Date

7-2015

Source Publication Title

Statistica Sinica

Volume

25

Issue

3

Start Page

993

End Page

1008

Publisher

Academia Sinica, Institute of Statistical Science

Peer Reviewed

1

Funder

The research of Guangming Pan was partially supported by the Ministry of Education, Singapore, under grant ARC 14/11. Tiejun Tong’s research was supported by Hong Kong Research grant HKBU202711 and Hong Kong Baptist University FRG grants FRG2/11-12/110 and FRG1/13-14/018. Lixing Zhu’s research was supported by a grant from the Research Grants Council of Hong Kong and a Faculty Research Grant (FRG) from Hong Kong Baptist University. The authors thank the Editor, an associate editor, and two reviewers for their helpful comments and suggestions that have substantially improved an early version of this manuscript.

DOI

10.5705/ss.2012.328

Link to Publisher's Edition

http://dx.doi.org/10.5705/ss.2012.328

ISSN (print)

10170405

ISSN (electronic)

19968507

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