In this work, a fully nonparametric geostatistical approach to estimate threshold-exceeding probabilities is proposed. We suggest to use the nonparametric local linear regression estimator, with a bandwidth selected by a method that takes the spatial dependence into account, to estimate the largescale variability (spatial trend) of a geostatistical process. To estimate the small-scale variability, a bias-corrected nonparametric estimate of the variogram is proposed. Finally, a bootstrap algorithm is used to estimate the probabilities of exceeding a threshold value at unsampled locations. The behavior of this approach is also evaluated through simulation and with an application to a real data set.

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