Nonparametric spatial prediction under stochastic sampling design

Abstract

In this work, the nonparametric kernel prediction will be considered for stochastic processes, when a random design is assumed for the spatial locations. We will check that, under rather general conditions, the mean-squared prediction error tends to be negligible, as the sample size increases. However, the use of the optimal bandwidth demands the estimation of unknown quantities, whose approximation in an accurate way often turns out to be difficult in practice. Hence, alternative cross-validation approaches will be provided for the selection of both local and global bandwidths. Numerical studies were carried out in order to analyse the performance of the nonparametric predictor for both simulated and real data.