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

Besson, Olivier and Abramovich, Yuri Invariance properties of the likelihood ratio for covariance matrix estimation in some complex elliptically contoured distributions. (2014) Journal of Multivariate Analysis, 124. 234-246. ISSN 0047-259X

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Official URL: http://dx.doi.org/10.1016/j.jmva.2013.10.024

Abstract

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(\R0|X), where R0 stands for the true covariance matrix of the observations $\X$, has a distribution which does not depend on R0 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 R0. Such invariance properties of LR (R0|X) were recently proven for a class of elliptically contoured distributions (ECD) in Abramovich and Besson (2013) and Bession and Abramovich (2013) where regularized CME were also presented. The aim of this paper is to derive the distribution of LR(R0|X) for other classes of ECD not covered yet, so as to make the EL approach feasible for a larger class of distributions.

Item Type:Article
Additional Information:Thanks to Elsevier editor. The definitive version is available at http://www.sciencedirect.com The original PDF of the article can be found at Journal of Multivariate Analysis website: http://www.sciencedirect.com/science/journal/0047259X/124/supp/C
HAL Id:hal-00936778
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Other partners > WR Systems (USA)
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Deposited By: Olivier Besson
Deposited On:27 Jan 2014 13:24

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