Parsimonious Compactly Supported Covariance Models in the Gauss Hypergeometric Class: Identifiability, Reparameterizations, and Asymptotic Properties

2025/06/16 by Moreno Bevilacqua, Christian Caamaño‐Carrillo, Bevilacqua, Moreno +5 · 1 citation
Environmental Science · Mathematics · #Soil Geostatistics and Mapping #Probability and Statistical Research

paper · pdf · doi:10.48550/arxiv.2506.13646

Abstract

We study covariance functions in the Gauss hypergeometric (GH) class, a flexible family that encompasses the Generalized Wendland (GW) and Matérn (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 GW family and admits compact-support reparameterizations that recover the 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.

Citations

• Fast simulation of Gaussian random fields with flexible correlation models in Euclidean spaces
• Matern and Generalized Wendland correlation models that parameterize hole effect, smoothness, and support
• Gaussian Whittle-Matérn fields on metric graphs
• The Gauss Hypergeometric Covariance Kernel for Modeling Second-Order Stationary Random Fields in Euclidean Spaces: its Compact Support, Properties and Spectral Representation
• Bayesian Fixed-domain Asymptotics for Covariance Parameters in a Gaussian Process Model
• Unifying Compactly Supported and Matern Covariance Functions in Spatial Statistics
• Beyond Matérn: On A Class of Interpretable Confluent Hypergeometric Covariance Functions
• SciPy 1.0: fundamental algorithms for scientific computing in Python
• WorldClim 2: new 1‐km spatial resolution climate surfaces for global land areas
• Computing hypergeometric functions rigorously
• Hanson-Wright inequality and sub-gaussian concentration
• The Role of the Range Parameter for Estimation and Prediction in\n Geostatistics
• Maximum likelihood estimation of models for residual covariance in spatial regression

Cited by

• Fast simulation of Gaussian random fields with flexible correlation models in Euclidean spaces

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