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Wendland（$\mathcal{GW}$）模型与Matérn（$\mathcal{MT}$）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$\mathcal{GW}$族的结构精化，且其紧支撑重参数化形式能以$\mathcal{MT}$模型为极限特例。我们进一步建立了固定域渐近下相关微遍历参数的最大似然估计量的强相合性与渐近正态性。针对气候数据的模拟实验与实证应用展示了所提模型的有限样本行为与实际性能。