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Unbiased risk estimation method for covariance estimation

Published online by Cambridge University Press:  25 July 2014

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.

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Type
Research Article
Copyright
© EDP Sciences, SMAI, 2014

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