Estimation of the inverse scatter matrix of an elliptically symmetric distribution

JOURNAL OF MULTIVARIATE ANALYSIS

卷:143

Article

Fourdrinier, Dominique¹  Mezoued, Fatiha²  Wells, Martin T.³ 

[1] Univ Rouen, Normandie Univ, LITIS, EA 4108, F-76801 St Etienne Du Rouvray, France

[2] Ecole Natl Super Stat & Econ Appl ENSSEA Ex INPS, Algiers, Algeria

[3] Cornell Univ, Dept Stat Sci, 1190 Comstock Hall, Ithaca, NY 14853 USA

关键词: Elliptically symmetric distributions;    High-dimensional statistics;    Moore-Penrose inverse;    Inverse scatter matrix;    Quadratic loss;    Singular sample covariance matrix;    Sample eigenvalues;    Stein-Half identity;   

DOI  :  10.1016/j.jmva.2015.08.012

来源: Elsevier

【 摘 要 】

We consider estimation of the inverse scatter matrices Sigma(-1) for high-dimensional elliptically symmetric distributions. In high-dimensional settings the sample covariance matrix S may be singular. Depending on the singularity of S. natural estimators of Sigma(-1) are of the form a S-1 or a S+ where a is a positive constant and S-1 and S+ are, respectively, the inverse and the Moore-Penrose inverse of S. We propose a unified estimation approach for these two cases and provide improved estimators under the quadratic loss tr((Sigma) over cap (-1) - Sigma(-1))(2). To this end, a new and general Stein-Haff identity is derived for the high-dimensional elliptically symmetric distribution setting. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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