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The current study aims to provide nonparametric estimators of the conditional variance and the dependence structure of a heteroscedastic spatial process. When assuming zero mean along the domain, the approximation of the variance can be addressed by linear smoothing of the squared observations. Then, the variogram can be estimated from the standardized data. In the presence of a non-zero deterministic trend, we suggest a modification of the latter method that involves the residuals obtained from a local linear estimation of the trend, together with corrections of the biases derived from the use of these residuals. This work includes the results of numerical studies carried out to check the performance of the proposed approach. In addition, the proposed methodology is applied to monthly precipitation data collected on the continental part of USA. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]