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 |
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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 |
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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 - UT3 (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) |
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Deposited On: | 15 Mar 2013 10:34 |
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