Asymptotically equivalent prediction in multivariate geostatistics

Cokriging is the common method of spatial interpolation (best linear unbiased prediction) in multivariate geostatistics. While best prediction has been well understood univariate statistics, literature for case elusive so far. The new challenges provided by modern datasets, being typically multivariate, call a deeper study cokriging. In particular, we deal with problem misspecified cokriging within framework fixed domain asymptotics. Specifically, provide conditions equivalence measures associated Gaussian random fields, index set compact d-dimensional Euclidean space. Such have over about 50 years statistics. We then focus on Matérn and Generalized Wendland classes matrix valued covariance functions, that very popular having parameters are crucial to interpolation, control mean square differentiability process. sufficient conditions, measures, relying these two classes. This enables identify asymptotically equivalent Our findings illustrated through simulation studies.