Estimation of covariance functions by a fully data-driven model selection procedure and its application to Kriging spatial interpolation of real rainfall data

In this paper, we propose a data-driven model selection approach for the nonparametric estimation of covariance functions under very general moments assumptions on the stochastic process. Observing i.i.d replications of the process at fixed observation points, we select the best estimator among a set of candidates using a penalized least squares estimation procedure with a fully data-driven penalty function, extending the work in Bigot et al. (Electron J Stat 4:822–855, 2010). We then provide a practical application of this estimate for a Kriging interpolation procedure to forecast rainfall data.