Influence diagnostics on a reparameterized t-Student spatial linear model

Abstract In this paper, we consider a spatial linear model under the multivariate t-Student distribution with finite second moment. This distribution, which contains the normal distribution, offers a more flexible framework for modeling spatial data. We use a reparametrized version of the multivariate t-Student distribution, so that the scale matrix corresponds to the covariance matrix of the spatial data. The main goal of this work is to develop influence measures to detect presence of influential observations and possible outliers, based on the likelihood displacement and on the score statistics. A heteroskedastic model is considered as a perturbation scheme to the covariance matrix of t-Student spatial linear model. Identifiability issues and robustness aspects of the maximum likelihood estimators are also discussed. The results are illustrated using a soybean yield real data and a simulation study.