We propose a new model for regression and dependence analysis when addressing spatial data with possibly heavy tails and an asymmetric marginal distribution. We first propose a stationary process with $t$ marginals obtained through scale mixing of a Gaussian process with an inverse square root process with Gamma marginals. We then generalize this construction by considering a skew-Gaussian process, thus obtaining a process with skew-t marginal distributions. For the proposed (skew) $t$ process we study the second-order and geometrical properties and in the $t$ case, we provide analytic expressions for the bivariate distribution. In an extensive simulation study, we investigate the use of the weighted pairwise likelihood as a method of estimation for the $t$ process. Moreover we compare the performance of the optimal linear predictor of the $t$ process versus the optimal Gaussian predictor. Finally, the effectiveness of our methodology is illustrated by analyzing a georeferenced dataset on maximum temperatures in Australia

中文翻译：

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使用（偏斜）t 过程的非高斯地质统计建模

在处理可能具有重尾和非对称边缘分布的空间数据时，我们提出了一种用于回归和相关性分析的新模型。我们首先提出了一个具有 $t$ 边际的平稳过程，该过程通过高斯过程与具有伽玛边际的平方根反过程的尺度混合获得。然后我们通过考虑 skew-Gaussian 过程来概括这种构造，从而获得具有 skew-t 边缘分布的过程。对于建议的（偏斜）$t$ 过程，我们研究二阶和几何特性，在 $t$ 情况下，我们提供二元分布的解析表达式。在广泛的模拟研究中，我们研究了使用加权成对似然作为估计 $t$ 过程的方法。此外，我们比较了 $t$ 过程的最佳线性预测器与最佳高斯预测器的性能。最后，通过分析澳大利亚最高温度的地理参考数据集来说明我们方法的有效性