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On the Expected Likelihood Approach for Assessment of Regularization Covariance Matrix

Abramovich, Yuri and Besson, Olivier On the Expected Likelihood Approach for Assessment of Regularization Covariance Matrix. (2015) IEEE Signal Processing Letters, 22 (6). 777-781. ISSN 1070-9908

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Official URL: http://dx.doi.org/10.1109/LSP.2014.2369232

Abstract

Regularization, which consists in shrinkage of the sample covariance matrix to a target matrix, is a commonly used and effective technique in low sample support covariance matrix estimation. Usually, a target matrix is chosen and optimization of the shrinkage factor is carried out, based on some relevant metric. In this letter, we rather address the choice of the target matrix. More precisely, we aim at evaluating, from observation of the data matrix, whether a given target matrix is a good regularizer. Towards this end, the expected likelihood (EL) approach is investigated. At a first step, we re-interpret the regularized covariance matrix estimate as the minimum mean-square error estimate in a Bayesian model where the target matrix serves as a prior. The likelihood function of the data is then derived, and the EL principle is subsequently applied. Over-sampled and under-sampled scenarios are considered.

Item Type:Article
Additional Information:Thanks to IEEE editor. (c) 2011 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. The definitive version is available at http://ieeexplore.ieee.org
HAL Id:hal-01131285
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)
Laboratory name:
Département d'Electronique, Optronique et Signal - DEOS (Toulouse, France) - Signal, Communication, Antenne et Navigation - SCAN
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Deposited By: Olivier Besson
Deposited On:13 Mar 2015 11:12

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