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.
"Nonparametric estimation of covariance functions by model selection." Electron. J. Statist. 4 822 - 855, 2010. https://doi.org/10.1214/09-EJS493