Nonparametric estimation of covariance functions by model selection

Details Nonparametric estimation of covariance functions by model selection Nonparametric estimation of covariance functions by model selection

2009-09-28

arxiv.org/abs/0909.5168v1

Mathematics

Statistics Theory

Scientific paper

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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