The Gaussian copula is a powerful tool that has been widely used to model spatial and/or temporal correlated data with arbitrary marginal distributions. However, this kind of model can potentially be too restrictive since it expresses a reflection symmetric dependence. In this paper, we propose a new spatial copula model that makes it possible to obtain random fields with arbitrary marginal distributions with a type of dependence that can be reflection symmetric or not. Particularly, we propose a new random field with uniform marginal distributions that can be viewed as a spatial generalization of the classical Clayton copula model. It is obtained through a power transformation of a specific instance of a beta random field which in turn is obtained using a transformation of two independent Gamma random fields. For the proposed random field, we study the second-order properties and we provide analytic expressions for the bivariate distribution and its correlation. Finally, in the reflection symmetric case, we study the associated geometrical properties. As an application of the proposed model we focus on spatial modeling of data with bounded support. Specifically, we focus on spatial regression models with marginal distribution of the beta type. In a simulation study, we investigate the use of the weighted pairwise composite likelihood method for the estimation of this model. Finally, the effectiveness of our methodology is illustrated by analyzing point-referenced vegetation index data using the Gaussian copula as benchmark. Our developments have been implemented in an open-source package for the \textsf{R} statistical environment.

翻译：高斯Copula是一种广泛用于建模具有任意边缘分布的空间和/或时间相关数据的强大工具。然而，这类模型可能具有过于严格的限制，因为它表达了反射对称依赖关系。本文提出一种新的空间Copula模型，该模型能够生成具有任意边缘分布且依赖类型可对称也可非对称的随机场。特别地，我们提出了一种新的具有均匀边缘分布的随机场，可视为经典Clayton Copula模型的空间推广。该模型通过对特定Beta随机场实例进行幂变换而获得，而该Beta随机场又通过两个独立Gamma随机场的变换得到。针对所提出的随机场，我们研究了其二阶性质，并给出了二元分布及其相关性的解析表达式。最后，在反射对称情形下，我们研究了相关的几何性质。作为所提模型的应用，我们重点关注有界支撑数据的空间建模，特别是边缘分布为Beta类型的空间回归模型。在模拟研究中，我们探究了加权成对复合似然方法用于该模型参数估计的效果。最后，通过以高斯Copula为基准分析点参考植被指数数据，验证了我们方法的有效性。我们的研究成果已在R统计环境的开源软件包中实现。