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A nonparametric procedure to estimate the conditional probability that a nonstationary geostatistical process exceeds a certain threshold value is proposed. The method consists of a bootstrap algorithm that combines conditional simulation techniques with nonparametric estimations of the trend and the variability. The nonparametric local linear estimator, considering a bandwidth matrix selected by a method that takes the spatial dependence into account, is used to estimate the trend. The variability is modeled estimating the conditional variance and the variogram from corrected residuals to avoid the biasses. The proposed method allows to obtain estimates of the conditional exceedance risk in non-observed spatial locations. The performance of the approach is analyzed by simulation and illustrated with the application to a real data set of precipitations in the USA.Supplementary materials accompanying this paper appear on-line. [ABSTRACT FROM AUTHOR]

In this work, we study the asymptotic properties of smoothed nonparametric kernel spectral density estimators for the spatial spectral density. We consider the case of continuous stationary spatial processes under a shrinking asymptotic framework. Expressions for the bias and the covariance structure are obtained and the implications for the edge effect bias of the choice of the kernel, bandwidth and spacing parameter in the design are also discussed, both for tapered and untapered estimates. Results are illustrated with a simulation study. [ABSTRACT FROM AUTHOR]