Open Access
2010 Nonparametric estimation of covariance functions by model selection
Jérémie Bigot, Rolando Biscay, Jean-Michel Loubes, Lilian Muñiz-Alvarez
Electron. J. Statist. 4: 822-855 (2010). DOI: 10.1214/09-EJS493


We propose a model selection approach for covariance estimation of a 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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Jérémie Bigot. Rolando Biscay. Jean-Michel Loubes. Lilian Muñiz-Alvarez. "Nonparametric estimation of covariance functions by model selection." Electron. J. Statist. 4 822 - 855, 2010.


Published: 2010
First available in Project Euclid: 8 September 2010

zbMATH: 1329.62365
MathSciNet: MR2684389
Digital Object Identifier: 10.1214/09-EJS493

Primary: 62G05 , 62G20

Keywords: Covariance estimation , Model selection , Oracle inequality

Rights: Copyright © 2010 The Institute of Mathematical Statistics and the Bernoulli Society

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