Invariance properties of the likelihood ratio for covariance matrix estimation in some complex elliptically contoured distributions

JOURNAL OF MULTIVARIATE ANALYSIS

卷:124

Article

Besson, Olivier¹  Abramovich, Yuri I.² 

[1] Univ Toulouse, ISAE, Dept Elect Optron & Signal, F-31055 Toulouse, France

[2] W R Syst Ltd, Fairfax, VA 22030 USA

关键词: Covariance matrix estimation;    Elliptically contoured distribution;    Expected likelihood;    Likelihood ratio;   

DOI  :  10.1016/j.jmva.2013.10.024

来源: Elsevier

【 摘 要 】

The likelihood ratio (LR) for testing if the covariance matrix of the observation matrix X is R has some invariance properties that can be exploited for covariance matrix estimation. purposes. More precisely, it was shown in Abramovich et al. (2004, 2007, 2007) that, in the Gaussian case, LR(R-0|X), where R-0 stands for the true covariance matrix of the observations X, has a distribution which does not depend on R-0 but only on known parameters. This paved the way to the expected likelihood (EL) approach, which aims at assessing and possibly enhancing the quality of any covariance matrix estimate (CME) by comparing its LR to that of R-0. Such invariance properties of LR(R-0|X) were recently proven for a class of elliptically contoured distributions (ECD) in Abramovich and Besson (2013) and Besson and Abramovich (2013) where regularized CME were also presented. The aim of this paper is to derive the distribution of LR(R-0|X) for other classes of ECD not covered yet, so as to make the EL approach feasible for a larger class of distributions. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free