Skip to Main content Skip to Navigation
Journal articles

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

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.
Document type :
Journal articles
Complete list of metadata

Cited literature [24 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00936778
Contributor : Open Archive Toulouse Archive Ouverte (oatao) <>
Submitted on : Monday, January 27, 2014 - 2:15:26 PM
Last modification on : Wednesday, January 31, 2018 - 2:02:07 PM
Long-term archiving on: : Sunday, April 9, 2017 - 12:08:58 AM

File

Besson_10737.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Olivier Besson, Yuri Abramovich. Invariance properties of the likelihood ratio for covariance matrix estimation in some complex elliptically contoured distributions. Journal of Multivariate Analysis, Elsevier, 2014, vol. 124, pp. 234-246. ⟨10.1016/j.jmva.2013.10.024⟩. ⟨hal-00936778⟩

Share

Metrics

Record views

176

Files downloads

328