Matern and Generalized Wendland correlation models that parameterize hole effect, smoothness, and support

TL;DR

This paper introduces two new families of correlation models that can capture negative dependencies, generalizing Matérn and Wendland models, with demonstrated improved estimation and prediction performance.

Contribution

The work develops two novel parametric correlation families that include negative dependencies and generalize existing models, establishing a link between them.

Findings

New models effectively capture hole effects.

Models show improved estimation accuracy.

Enhanced prediction performance on synthetic and real data.

Abstract

A huge literature in statistics and machine learning is devoted to parametric families of correlation functions, where the correlation parameters are used to understand the properties of an associated spatial random process in terms of smoothness and global or compact support. However, most of current parametric correlation functions attain only non-negative values. This work provides two new families that parameterize negative dependencies (aka hole effects), along with smoothness, and global or compact support. They generalize the celebrated Mat\'ern and Generalized Wendland models, respectively, which are attained as special cases. A link between the two new families is also established, showing that a specific reparameterization of the latter includes the former as a special limit case. Their performance in terms of estimation accuracy and goodness of best linear unbiased prediction is illustrated through synthetic and real data.