Bandwidth selection for local linear estimation of the spatial trend

The estimation of the large-scale variability (spatial trend) of a geostatistical process can be accomplished by using nonparametric regression. In this work, we will focus on the local linear estimation of the trend function and, more specifically, on the selection of the bandwidth matrix involved. An overview of approaches suggested for the latter aim will be outlined and additional alternatives will be introduced, based on correcting the cross-validation selector. Numerical studies will be carried out for comparison of the different proposals and an application to a real data set will be also included to illustrate their behavior in practice.