The current work provides a nonparametric resampling procedure for approximating the (unconditional) probability that a spatial variable surpasses a prefixed threshold value. The existing approaches for the latter issue require assuming constant variance throughout the observation region, thus our proposal has been designed to be valid under heteroscedasticity of the spatial process. To develop the new methodology, nonparametric estimates of the variance and the semivariogram functions are computed by using bias-corrected residuals, which are then employed to derive bootstrap replicates for approximating the aforementioned risk. The performance of this mechanism is checked through numerical studies with simulated data, where a comparison with a semiparametric method is also included. In addition, the practical application of this approach is exemplified by estimating the risk of rainwater accumulation in the United States, during a specific period.

当前的工作提供了一种非参数重采样程序，用于近似估计空间变量超过前缀阈值的（无条件）概率。针对后一个问题的现有方法要求在整个观察区域内假设恒定的方差，因此我们的建议被设计为在空间过程的异方差下有效。为了开发新的方法，通过使用偏差校正残差计算方差和半变异函数的非参数估计，然后将其用于导出自举重复以近似上述风险。通过对模拟数据进行数值研究来检查该机制的性能，其中还包括与半参数方法的比较。此外，