Adaptive Covariance Estimation with model selection

2012/03/01 by Rolando Biscay, Biscay, Rolando, Hélène Lescornel +3
Mathematics · #FOS: Mathematics #Statistics Theory (math.ST) #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1203.0107

arxiv created 2012/03/01 · arxiv updated 2012/03/05

Abstract

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.

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