In spatial statistics, the kriging predictor is the best linear predictor at unsampled locations, but not the optimal predictor for non-Gaussian processes. In this paper, we introduce a copula-based multiple indicator kriging model for the analysis of non-Gaussian spatial data by thresholding the spatial observations at a given set of quantile values. The proposed copula model allows for flexible marginal distributions while modeling the spatial dependence via copulas. We show that the covariances required by kriging have a direct link to the chosen copula function. We then develop a semiparametric estimation procedure. The proposed method provides the entire predictive distribution function at a new location, and thus allows for both point and interval predictions. The proposed method demonstrates better predictive performance than the commonly used variogram approach and Gaussian kriging in the simulation studies. We illustrate our methods on precipitation data in Spain during November 2019, and heavy metal dataset in topsoil along the river Meuse, and obtain probability exceedance maps.

在空间统计中，克里金预测器是未采样位置的最佳线性预测器，但不是非高斯过程的最佳预测器。在本文中，我们引入了一种基于 copula 的多指标克里金模型，通过在给定的分位数值集上对空间观察进行阈值化来分析非高斯空间数据。所提出的 copula 模型允许灵活的边缘分布，同时通过 copula 对空间依赖性进行建模。我们表明克里金法所需的协方差与所选的 copula 函数有直接联系。然后我们开发了一个半参数估计程序。所提出的方法在新位置提供整个预测分布函数，因此允许点和区间预测。与模拟研究中常用的变异函数方法和高斯克里金法相比，所提出的方法具有更好的预测性能。我们举例说明了我们对 2019 年 11 月西班牙降水数据和默兹河沿岸表土重金属数据集的方法，并获得了概率超标图。