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Unbiased risk estimation method for covariance estimation

Published online by Cambridge University Press:  25 July 2014

Hélène Lescornel ,
Jean-Michel Loubes  and
Claudie Chabriac
Hélène Lescornel
Affiliation:
Institut de Mathématiques de Toulouse UMR 5219, 31062 Toulouse, Cedex 9, France. helene.lescornel@math.univ-toulouse.fr; loubes@math.univ-toulouse.fr; chabriac@univ-tlse2.fr
Jean-Michel Loubes
Affiliation:
Institut de Mathématiques de Toulouse UMR 5219, 31062 Toulouse, Cedex 9, France. helene.lescornel@math.univ-toulouse.fr; loubes@math.univ-toulouse.fr; chabriac@univ-tlse2.fr
Claudie Chabriac
Affiliation:
Institut de Mathématiques de Toulouse UMR 5219, 31062 Toulouse, Cedex 9, France. helene.lescornel@math.univ-toulouse.fr; loubes@math.univ-toulouse.fr; chabriac@univ-tlse2.fr
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Abstract

We consider a model selection estimator of the covariance of a random process. Using the Unbiased Risk Estimation (U.R.E.) method, we build an estimator of the risk which allows to select an estimator in a collection of models. Then, we present an oracle inequality which ensures that the risk of the selected estimator is close to the risk of the oracle. Simulations show the efficiency of this methodology.

Keywords

Covariance estimationmodel selectionU.R.E. method
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 18 , 2014 , pp. 251 - 264
Copyright
© EDP Sciences, SMAI, 2014

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