The Empirical Likelihood method applied to covariance matrix estimation

Fréderic Pascal (1, 2) , Hugo Harari-Kermadec (3, 4) , Pascal Larzabal (5)

1 L2S - Laboratoire des signaux et systèmes
2 SONDRA - Sondra, CentraleSupélec, Université Paris-Saclay (COmUE)
3 CREST - Centre de Recherche en Économie et Statistique
4 ENS Cachan - École normale supérieure - Cachan
5 SATIE - Systèmes et Applications des Technologies de l'Information et de l'Energie

This paper presents a new estimation scheme for signal processing problems in unknown noise field. The Empirical Likelihood has been introduced in the mathematical community, but, surprisingly, it is still unknown in the signal processing community. This estimation method is an alternative to estimate unknown parameters without using a model for the probability density function. The aim of this paper is twofold: first, the Empirical Likelihood theory is presented and revisited thanks to the moment method. Its properties are derived. Second, to emphasize all the potentiality of this method, we address the problem of Toeplitz matrix estimation: this leads us to obtain improved estimates in comparison to conventional ones, as shown in simulations.

Mots clés: Maximum Likelihood; Empirical Likelihood; structured parameters estimation; non-Gaussian noise; covariance matrix estimation

Domaines: Electromagnétisme

Fréderic Pascal, Hugo Harari-Kermadec, Pascal Larzabal. The Empirical Likelihood method applied to covariance matrix estimation. Signal Processing, 2010, 90 (2), pp. 566-578. ⟨10.1016/j.sigpro.2009.07.028⟩. ⟨hal-00556225⟩