The classical linear model of coregionalization and its simpler counterpart known as the proportional covariance model, or intrinsic correlation model, have become standard tools in many areas of application for the analysis of multivariate spatial data. Despite the merits of this model, it guarantees optimal predictions only in the case of Gaussian data and can lead to erroneous conclusions in all other circumstances, in particular in the presence of skew data. To deal with multivariate geostatistical data showing some degree of skewness, this article proposes a latent spatial factor model in which all finite‐dimensional marginal distributions are multivariate unified skew‐normal. For this model, we can write the log‐likelihood function of the data and implement a maximum likelihood estimation procedure which enables the simultaneous estimation of all parameters of the model. Moreover, we also show how the computational burden involved in the nonlinear mapping of the latent factors can be substantially reduced by exploiting a linearity property of the predictions. The sampling performances of the inferential procedures are investigated in some thorough simulation studies, and an application to radioactive contamination data is presented to show the flexibility of the model. Detailed derivations of our results are available as Supplementary Material.

中文翻译：

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统一的偏正态地统计因子模型

共区域化的经典线性模型及其更简单的对应模型（称为比例协方差模型或本征相关模型）已成为许多领域中用于分析多元空间数据的标准工具。尽管该模型有其优点，但它仅在高斯数据的情况下可以保证最佳预测，并且在所有其他情况下，尤其是在存在偏斜数据的情况下，都可能导致错误的结论。为了处理显示一定程度偏斜的多元地统计数据，本文提出了一个潜在的空间因子模型，其中所有有限维边际分布均为多元统一偏斜正态。对于此模型，我们可以编写数据的对数似然函数，并执行最大似然估计程序，该程序可以同时估计模型的所有参数。此外，我们还展示了如何通过利用预测的线性特性来显着减少潜在因子的非线性映射中涉及的计算负担。在一些彻底的模拟研究中对推论程序的采样性能进行了研究，并提出了对放射性污染数据的应用，以显示该模型的灵活性。我们的结果的详细推导可作为补充材料获得。我们还展示了如何通过利用预测的线性特性来显着减少潜在因子的非线性映射中涉及的计算负担。在一些彻底的模拟研究中对推论程序的采样性能进行了研究，并提出了对放射性污染数据的应用，以显示该模型的灵活性。我们的结果的详细推导可作为补充材料获得。我们还展示了如何通过利用预测的线性特性来显着减少潜在因子的非线性映射中涉及的计算负担。在一些彻底的模拟研究中对推论程序的采样性能进行了研究，并提出了对放射性污染数据的应用，以显示该模型的灵活性。我们的结果的详细推导可作为补充材料获得。