Nonparametric estimation of covariance functions by model selection
Statistics Theory
2009-09-29 v1 Statistics Theory
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.
Cite
@article{arxiv.0909.5168,
title = {Nonparametric estimation of covariance functions by model selection},
author = {Jérémie Bigot and Rolando Biscay and Jean-Michel Loubes and Lilian Muniz Alvarez},
journal= {arXiv preprint arXiv:0909.5168},
year = {2009}
}