Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Shrinkage estimation of large dimensional precision matrix using random matrix theory

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

2015

Source Publication Title

Statistica Sinica

Volume

25

Issue

3

Start Page

993

End Page

1008

Publisher

Academia Sinica, Institute of Statistical Science

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

This document is currently not available here.

Share

COinS