Abstract

The generalized Wendland covariance model is a flexible compactly supported covariance model that allows for a continuous parameterization of smoothness of the underlying Gaussian random field, and includes the celebrated Mat & eacute;rn as a special limit case. However, the generalized Wendland model does not cover the full range of validity of the smoothness parameter of the Mat & eacute;rn model. In this paper, we provide new necessary and sufficient conditions of validity of the generalized Wendland model that allows to fill this gap. The effectiveness of our proposal is illustrated through a simulation study and a re-analysis of a large geo-referenced dataset of yearly total precipitation anomalies.