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Nonparametric estimation of covariance functions by model selection

Bigot, Jérémie and Biscay, Rolando and Loubes, Jean-Michel and Muñiz-Alvarez, Lilian Nonparametric estimation of covariance functions by model selection. (2010) Electronic Journal of Statistics, 4. 822-855. ISSN 1935-7524

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Official URL: http://dx.doi.org/10.1214/09-EJS493

Abstract

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.

Item Type:Article
Additional Information:Thanks to Institute of Mathematical Statistics editor. The definitive version is available at http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.ejs/1283952133
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National des Sciences Appliquées de Toulouse - INSA (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Other partners > Universidad de La Habana - UH (CUBA)
Other partners > Universidad de Valparaiso - UV (CHILE)
Laboratory name:
Statistics:download
Deposited By: Jérémie Bigot
Deposited On:15 Mar 2013 10:34

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