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Nonparametric bootstrap approach for unconditional risk mapping under heteroscedasticity

Abstract:

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.