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Pré-Publication, Document De Travail Année : 2009

Nonparametric estimation of covariance functions by model selection

Résumé

We propose a model selection approach for covariance estimation of a multi-dimensional stochastic process. Under very general assumptions, observing i.i.d replications of the process at fixed observation points, we construct an estimator of the covariance function by expanding the process onto a collection of basis functions. We study the non asymptotic property of this estimate and give a tractable way of selecting the best estimator among a possible set of candidates. The optimality of the procedure is proved via an oracle inequality which warrants that the best model is selected.
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Dates et versions

hal-00420301 , version 1 (28-09-2009)

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Jérémie Bigot, Rolando Biscay, Jean-Michel Loubes, Lilian Muniz Alvarez. Nonparametric estimation of covariance functions by model selection. 2009. ⟨hal-00420301⟩
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