Non-Homogeneity Estimation and Universal Kriging on the Sphere

TL;DR

This paper introduces a method to estimate non-homogeneity on the sphere using IRF theory, enabling the development of a universal kriging approach that outperforms ordinary kriging in non-homogeneous cases.

Contribution

It proposes a graphical estimation method for non-homogeneity and develops an IRF universal kriging procedure for spherical spatial data.

Findings

IRF universal kriging performs better than ordinary kriging in non-homogeneous scenarios

The graphical estimation method effectively captures non-homogeneity levels

Simulation results validate the advantages of the proposed approach

Abstract

Kriging is a widely recognized method for making spatial predictions. On the sphere, popular methods such as ordinary kriging assume that the spatial process is intrinsically homogeneous. However, intrinsic homogeneity is too strict in many cases. This research uses intrinsic random function (IRF) theory to relax the homogeneity assumption. A key component of modeling IRF processes is estimating the degree of non-homogeneity. A graphical approach is proposed to accomplish this estimation. With the ability to estimate non-homogeneity, an IRF universal kriging procedure can be developed. Results from simulation studies are provided to demonstrate the advantage of using IRF universal kriging as opposed to ordinary kriging when the underlying process is not intrinsically homogeneous.