On the Estimation of Anisotropic Covariance Functions on Compact Two-Point Homogeneous Spaces

TL;DR

This paper extends the asymptotic theory for anisotropic covariance estimators from the 2D sphere to all connected, compact two-point homogeneous spaces, broadening the applicability of such statistical methods.

Contribution

It generalizes existing asymptotic results for spline-type anisotropic covariance estimators from the sphere to a wider class of homogeneous spaces.

Findings

Generalized asymptotic theory to all connected, compact two-point homogeneous spaces.

Provided mathematical framework for anisotropic covariance estimation on these spaces.

Extended previous results from the 2D sphere case.

Abstract

In this paper, the asymptotic theory presented in (Caponera et al., 2022) for spline-type anysotropic covariance estimator on the 2-dimensional sphere is generalized to the case of connected and compact two-point homogeneous spaces.