The ordering of spatial data and the detection of multiple outliers

In this article we suggest a unified approach to the exploratory analysis of spatial data. Our technique is based on a forward search algorithm that orders the observations from those most in agreement with a specified autocorrelation model to those least in agreement with it. This leads to the identification of spatial outliers-that is, extreme observations with respect to their neighboring values-and of nonstationary pockets. In particular, the focus of our analysis is on spatial prediction models. We show that standard deletion diagnostics for prediction are affected by masking and swamping problems when multiple outliers are present. The effectiveness of the suggested method in detecting masked multiple outliers, and more generally in ordering spatial data, is shown by means of a number of simulated datasets. These examples clearly reveal the power of our method in getting inside the data in a way which is more simple and powerful than it would be using standard diagnostic procedures. Furthermore, the behavior of our algorithm under the null hypothesis of no outliers is investigated through a Monte Carlo experiment. Such simulations are also used to build envelopes for the forward search.