Outliers detection in multivariate spatial linear models

In geostatistics, detecting atypical observations is of special interest due to the changes they can cause in environmental and geological patterns. Several methods for detecting them have been already suggested for the univariate spatial case. However, the problem is more complicated when various variables are observed simultaneously and the spatial correlation among them must be taken into account. The aim of this paper is to detect outliers and influential observations in multivariate spatial linear models. For this purpose, we derive and explore two different methods. First, a multivariate version of the forward search algorithm is given, where locations with outliers are detected in the last steps of the procedure. Next, we derive influence measures to assess the impact of the observations on the multivariate spatial linear model. The procedures are easy to compute and to interpret by means of graphical representations. Finally, an example and a Monte Carlo study illustrate the performance of these methods for identification of outliers in multivariate spatial linear models.