Extending the generalized Wendland covariance model

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 Matérn as a special limit case. However, the generalized Wendland model does not cover the full range of validity of the smoothness parameter of the Matérn 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.