Parsimonious Compactly Supported Covariance Models in the Gauss Hypergeometric Class: Identifiability, Reparameterizations, and Asymptotic Properties
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915863526899712 |
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| author | Bevilacqua, Moreno Caamaño-Carrillo, Christian Faouzi, Tarik Emery, Xavier |
| author_facet | Bevilacqua, Moreno Caamaño-Carrillo, Christian Faouzi, Tarik Emery, Xavier |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_13646 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Parsimonious Compactly Supported Covariance Models in the Gauss Hypergeometric Class: Identifiability, Reparameterizations, and Asymptotic Properties Bevilacqua, Moreno Caamaño-Carrillo, Christian Faouzi, Tarik Emery, Xavier Methodology 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. |
| title | Parsimonious Compactly Supported Covariance Models in the Gauss Hypergeometric Class: Identifiability, Reparameterizations, and Asymptotic Properties |
| topic | Methodology |
| url | https://arxiv.org/abs/2506.13646 |