Spatial linear models have been applied in numerous fields such as agriculture, geoscience and environmental sciences, among many others. Spatial dependence structure modelling, using a geostatistical approach, is an indispensable tool to estimate the parameters that define this structure. However, this estimation may be greatly affected by the presence of atypical observations in the sampled data. The purpose of this paper is to use diagnostic techniques to assess the sensitivity of the maximum-likelihood estimators, covariance functions and linear predictor to small perturbations in the data and/or the spatial linear model assumptions. The methodology is illustrated with two real data sets. The results allowed us to conclude that the presence of atypical values in the sample data have a strong influence on thematic maps, changing the spatial dependence structure.

In the present paper, a novel spatial quantile regression model based on the Birnbaum–Saunders distribution is formulated. This distribution has been widely studied and applied in many fields. To formulate such a spatial model, a parameterization of the multivariate Birnbaum–Saunders distribution, where one of its parameters is associated with the quantile of the respective marginal distribution, is established. The model parameters are estimated by the maximum likelihood method. Finally, a data set is applied for illustrating the formulated model.