Modern multivariate statistical analysis, a graduate course and handbook
Modern multivariate statistical analysis, a graduate course and handbook
Robust shrinkage estimation for elliptically symmetric distributions with unknown covariance matrix
Journal of Multivariate Analysis
A well-conditioned estimator for large-dimensional covariance matrices
Journal of Multivariate Analysis
Improved estimation of a covariance matrix in an elliptically contoured matrix distribution
Journal of Multivariate Analysis
Singular random matrix decompositions: distributions
Journal of Multivariate Analysis
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
GLRT-Based Detection-Estimation for Undersampled Training Conditions
IEEE Transactions on Signal Processing - Part I
Unified Framework to Regularized Covariance Estimation in Scaled Gaussian Models
IEEE Transactions on Signal Processing
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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.