Semi-parametric pairwise inference methods in spatial models based on copulas

Abstract

In this paper, semi-parametric models based on copulas are considered for the modeling of stationary and isotropic spatial random fields. To this end, a general family of multivariate distributions is introduced in which the dependence structure between any finite sets of locations is modeled via a copula and where the strength of the relationships between any two locations is controlled by a link function. Because the density of most of the multivariate spatial copulas is untractable, it is proposed that inferential procedures for these models be based on a pairwise approach taking into account the bivariate densities only. Specifically, a rank-based estimation procedure using the so-called pairwise likelihood is proposed and a semi-parametric spatial interpolation method for the prediction at un-sampled locations is developed; both methods are investigated with the help of simulated spatial random fields. The usefulness of the newly introduced tools is illustrated on the Meuse river data.