Characteristics of some isotropic covariance models with negative values

Abstract

In the literature, most of the classical covariance models characterised by negative values were derived by utilising the Bessel functions, on the other hand, recently, other classes of models with negative correlation were obtained through the difference between two covariance functions. However, although for the former, the analytic features, such as their absolute minimum values, were completely explored, for the latter these aspects have to be still investigated. In this paper, starting from the admissibility conditions and the general characteristics of three wide families of isotropic covariance models, based on the difference of Gaussian, exponential and rational models, their absolute minimum, as a function of the dimension of the Euclidean space in which they are defined, is provided. Consequently, the minimum values for the most common Euclidean dimensional spaces are given as special cases. These results fill the theoretical gap related to the analysed classes of correlation models with negative values and then can support their use. A simulation study and an application to a real data set are also presented to assess performance in terms of prediction accuracy.