Nonparametric estimation of covariance functions by model selection

2009/09/28 by Jérémie Bigot, Bigot, Jérémie, Rolando Biscay +5
Mathematics · #62G05 #62G20 #FOS: Mathematics #Statistics Theory (math.ST) #math.ST #msc:62G05 #msc:62G20 #stat.TH

paper · pdf · doi:10.48550/arxiv.0909.5168

arxiv created 2009/09/28 · arxiv updated 2009/12/01

Abstract

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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