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Geostatistical prediction through convex combination of Archimedean copulas
Spatial Statistics ( IF 2.3 ) Pub Date : 2020-12-30 , DOI: 10.1016/j.spasta.2020.100488
B. Sohrabian

A common problem in geostatistics is to interpolate a variable at unsampled locations using available data. Kriging has been the conventional method of solving this problem by providing the weighted average of samples, which is determined by minimizing the estimation variance. Kriging variance is a function of the samples’ spatial configuration and the variable’s spatial dependence structure. The latter is described by covariance that reduces complex dependence structures of natural phenomena to a single measure, introducing substantial simplifications. Another issue about kriging is that its variance does not depend on the sample values. Therefore, applying new methods such as spatial copulas that better describe the spatial dependence structure of variables and take advantage of sample values and spatial dependence structure would be helpful. This study compares prediction through the convex combination of Archimedean copulas to kriging using seven variables of the Jura data set. The empirical marginal distribution of variables and fitted kernel density estimates based on the Gaussian, triangular, Epanechnikov and gamma functions were used to investigate the effects of margins on the results. The mixed copulas were capable of describing various types of dependencies with asymmetric upper and lower tails. However, the Gaussian copula failed to explain the spatial dependence structure of variables and had the worst results among the copula-based approaches. The application of empirical marginal distribution of variables has generally given better results than the fitted models. For variables with large ratios of nugget effect to sill, in general, the copula-based approaches showed an advantage over kriging due to better reproduction of the mean values and distributions of the variables, having lower mean squared errors and higher correlation coefficients between the predicted and observed values. On the other hand, for variables with small nugget effects, kriging has better performance regarding all criteria except for the mean value reproduction. This study suggests using a convex combination of Archimedean copulas to predict variables with significant nugget effects.



中文翻译:

通过阿基米德系算子的凸组合进行地统计学预测

地统计学中的一个常见问题是使用可用数据在未采样位置内插变量。克里格法一直是通过提供样本的加权平均值来解决此问题的常规方法,该加权平均值是通过最小化估计方差来确定的。Kriging方差是样本的空间配置和变量的空间依赖性结构的函数。后者通过协方差来描述,该协方差将自然现象的复杂依赖性结构减少到一个量度,从而带来了极大的简化。关于克里金法的另一个问题是其方差不取决于样本值。因此,应用新方法(例如空间关联函数)可以更好地描述变量的空间依赖性结构并利用样本值和空间依赖性结构将很有帮助。这项研究使用朱拉(Jura)数据集的七个变量,将阿基米德系系的凸组合与克里金法的预测进行了比较。基于高斯函数,三角函数,Epanechnikov函数和gamma函数的变量的经验边际分布和拟合的核密度估计用于研究边距对结果的影响。混合的系词能够描述具有不对称的上尾巴和下尾巴的各种类型的依存关系。但是,高斯copula不能解释变量的空间依赖性结构,并且在基于copula的方法中结果最差。经验边际变量的应用通常比拟合模型给出更好的结果。通常,对于具有较大的金块效应与门槛比率的变量,基于copula的方法显示出优于kriging的优势,这是因为均值的更好再现和变量的分布,均方误差更低,而预测值和观察值之间的相关系数更高。另一方面,对于具有较小块金效应的变量,克里金法在除平均值再现之外的所有条件下均具有更好的性能。这项研究建议使用阿基米德系系的凸组合来预测具有显着金块效应的变量。克里金法在所有标准上均具有更好的性能,但均值再现除外。这项研究建议使用阿基米德系系的凸组合来预测具有显着金块效应的变量。克里金法在所有标准上均具有更好的性能,但均值再现除外。这项研究建议使用阿基米德系系的凸组合来预测具有显着金块效应的变量。

更新日期:2021-01-11
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