In this work, a fully nonparametric geostatistical approach to estimate threshold exceeding probabilities is proposed. To estimate the large-scale variability (spatial trend) of the process, the nonparametric local linear regression estimator, with the bandwidth selected by a method that takes the spatial dependence into account, is used. A bias-corrected nonparametric estimator of the variogram, obtained from the nonparametric residuals, is proposed to estimate the small-scale variability. Finally, a bootstrap algorithm is designed to estimate the unconditional probabilities of exceeding a threshold value at any location. The behavior of this approach is evaluated through simulation and with an application to a real data set.

翻译：本文提出了一种完全非参数的地质统计方法，用于估计阈值超越概率。为估计过程的大尺度变异性（空间趋势），采用非参数局部线性回归估计量，并通过考虑空间依赖性的方法选择带宽。基于非参数残差提出变差函数的偏差校正非参数估计量，以估计小尺度变异性。最后，设计自举算法来估计任意位置超越阈值水平的无条件概率。该方法的性能通过模拟实验及实际数据集应用进行了评估。