Radial positive definite functions are of importance both as the characteristic functions of spherically symmetric probability distributions, and as the correlation functions of isotropic random fields. The Euclid's hat functionhn(||x||),x[set membership, variant]n, is the self-convolution of an...

Handcock & Stein (1993) introduced the Matern family of spatial correlations into statistics as a flexible parametric class with one parameter determining the smoothness of the paths of the underlying spatial field. We document the varied history of this family, which includes contributions by...

Probabilistic forecasts of continuous variables take the form of predictive densities or predictive cumulative distribution functions. We propose a diagnostic approach to the evaluation of predictive performance that is based on the paradigm of "maximizing the sharpness of the predictive...

We present general results on the identifiability of finite mixtures of elliptical distributions under conditions on the characteristic generators or density generators. Examples include the multivariate "t"-distribution, symmetric stable laws, exponential power and Kotz distributions. In each...

abstract This letter considers stationary local approximations to intrinsically stationary random functions on . For any continuous variogram [gamma] and any ball in , there exists a covariance function with compact support whose respective variogram is arbitrarily close to [gamma] when...