Nonparametric spatial prediction under stochastic sampling design

In this work, the nonparametric kernel prediction will be considered for spatial stochastic processes when a stochastic sampling design is assumed for selection of locations. We will prove that under rather general conditions, the mean-squared prediction error tends to be negligible as the sample size increases. However, use of the optimal bandwidth demands the estimation of unknown quantities, whose accurate approximation can often 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.