Inference in Spatial Models: Applicability and Comparison of the Wendland and Matérn Covariance Families

Abstract

This paper investigates inference and diagnostic procedures in linear Gaussian spatial models using the Wendland family of covariance functions, compared with the Matérn family, as a spatial dependence structure. We extend the Spatial Dependency Index (SDI) and derive expressions for the practical range for both covariance families, establishing explicit relationships between the range and the decay parameter. A local influence diagnostic approach is employed to assess the sensitivity of maximum likelihood estimators. To determine cutoff values for identifying potentially influential observations, we propose a Jackknife-after-Bootstrap resampling method-a technique not yet applied in this context. The methodology is illustrated through an application to a soybean yield dataset. Our results indicate that the Wendland covariance family performs satisfactorily under Gaussian spatial model assumptions, offering a competitive alternative to the Matérn family, particularly in terms of computational efficiency due to its compact support.