Conditions on which cokriging does not do better than kriging

There is a vast literature on analyzing univariate spatial data by modeling, inference, and prediction in the past decades. While statistical modeling and inference with multivariate spatial data have been well developed, spatial prediction using multivariate spatial data called cokriging is relatively less investigated. Cokriging is usually considered to be superior to kriging, but there are not many theoretical studies that investigate how good cokriging is over kriging or when cokriging does not better than kriging. In this work, we provide explicit conditions on the covariance parameters and sampling schemes under an intrinsic coregionalization covariance model, with which cokriging does not better than kriging. Simulation studies and real data examples are also introduced to support our theoretical findings.