We study covariance functions in the Gauss hypergeometric ($\mathcal{GH}$) class, a flexible family that encompasses the Generalized Wendland ($\mathcal{GW}$) and Matérn ($\mathcal{MT}$) models. We derive sharp validity conditions, providing a complete characterization of the admissible parameter space, and show that the model exhibits structural identifiability issues under both increasing- and fixed-domain asymptotics. To resolve this issue, we introduce a parsimonious compactly supported subclass selected via a maximum integral range criterion. The resulting hypergeometric model can be viewed as a structural refinement of the $\mathcal{GW}$ family and admits compact-support reparameterizations that recover the $\mathcal{MT}$ model as a limit case. We further establish strong consistency and asymptotic normality of the maximum likelihood estimator of the associated microergodic parameter under fixed-domain asymptotics. Simulation experiments and a real-data application to climate data illustrate the finite-sample behavior and practical performance of the proposed model.

翻译：本文研究高斯超几何（$\mathcal{GH}$）类协方差函数，该灵活族包含广义温德兰（$\mathcal{GW}$）模型与马特恩（$\mathcal{MT}$）模型。我们推导出严格的合法性条件，完整刻画了容许参数空间，并证明该模型在递增域与固定域渐近框架下均存在结构可识别性问题。为解决此问题，我们通过最大积分范围准则选取一个简约的紧支撑子类。所得超几何模型可视为$\mathcal{GW}$族的结构改进，其紧支撑重参数化形式能以马特恩模型为极限情形。进一步，我们在固定域渐近框架下建立了对应微遍历参数极大似然估计的强相合性与渐近正态性。通过模拟实验与气候数据实证分析，展示了所提模型的有限样本特性与实际性能。