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

TL;DR

This paper introduces a new class of covariance models within the Gauss hypergeometric family, addressing identifiability issues and establishing their asymptotic properties, with demonstrated practical advantages through simulations and climate data application.

Contribution

It develops a parsimonious, compactly supported hypergeometric covariance model with reparameterizations, resolving identifiability problems and proving asymptotic properties of estimators.

Findings

Complete characterization of admissible parameter space.

Structural identifiability issues are addressed with a new subclass.

Model shows strong consistency and asymptotic normality of estimators.

Abstract

We study covariance functions in the Gauss hypergeometric ($\mathcal{GH}$) class, a flexible family that encompasses the Generalized Wendland ($\mathcal{GW}$) and Mat\'ern ($\mathcal{MT}$) 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.