Unifying compactly supported and Matérn covariance functions in spatial statistics

The Matérn family of covariance functions has played a central role in spatial statistics for decades, being flexible parametric class with one parameter determining the smoothness paths underlying field. This paper proposes functions, which stems from reparameterization generalized Wendland family. As case, proposed allows continuous parameterization Gaussian random field, additionally compactly supported. More importantly, we show that generalizes model is attained as special limit case. implies (reparametrized) Generalized more than an extra-parameter switching to globally supported functions. Our numerical experiments elucidate speed convergence model. We also inspect asymptotic distribution maximum likelihood method when estimating parameters models under both increasing and fixed domain asymptotics. effectiveness our proposal illustrated by analyzing georeferenced dataset mean temperatures over region French, performing re-analysis large point referenced yearly total precipitation anomalies.