Adaptive Covariance Estimation with model selection.

Rolando Biscay (1, 2) , Hélène Lescornel (3) , Jean-Michel Loubes (3)

1 IMFAV-DEUV - Departamento de Estadística Universidad de Valparaíso
2 Institute of Mathematics, Physics and Cybernetics
3 IMT - Institut de Mathématiques de Toulouse UMR5219

We provide in this paper a fully adaptive penalized procedure to select a covariance among a collection of models observing i.i.d replications of the process at fixed observation points. For this we generalize previous results of Bigot and al. and propose to use a data driven penalty to obtain an oracle inequality for the estimator. We prove that this method is an extension to the matricial regression model of the work by Baraud.

Mots clés: adaptive procedure; covariance estimation; model selection; adaptive procedure .

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Rolando Biscay, Hélène Lescornel, Jean-Michel Loubes. Adaptive Covariance Estimation with model selection.. Mathematical Methods of Statistics, 2012, 21 (4), pp.283-297. ⟨10.3103/S1066530712040023⟩. ⟨hal-00675273⟩