Robust methods for the analysis of spatially autocorrelated data

In this paper we propose a new robust technique for the analysis of spatial data through simultaneous autoregressive (SAR) models, which extends the Forward Search approach of Cerioli and Riani (1999) and Atkinson and Riani (2000). Our algorithm starts from a subset of outlier-free observations and then selects additional observations according to their degree of agreement with the postulated model. A number of useful diagnostics which are monitored along the search help to identify masked spatial outliers and high leverage sites. In contrast to other robust techniques, our method is particularly suited for the analysis of complex multidimensional systems since each step is performed through statistically and computationally efficient procedures, such as maximum likelihood. The main contribution of this paper is the development of joint robust estimation of both trend and autocorrelation parameters in spatial linear models. For this purpose we suggest a novel definition of the elemental sets of the Forward Search, which relies on blocks of contiguous spatial locations.