Comparison of robust detection techniques for local outliers in multivariate spatial data

Spatial data are characterized by statistical units, with known geographical positions, on which non spatial attributes are measured. Spatial data may contain two types of atypical observations: global and/or local outliers. The attribute values of a global outlier are outlying with respect to the values taken by the majority of the data points while the attribute values of a local outlier are extreme when compared to those of its neighbors.

Usual outlier detection techniques may be used to find global outliers as the geographical positions of the data is not taken into account in this specific search. The detection of local outliers is more complex, especially when there are more than one non spatial attributes. This talk focuses on local detection with two main objectives.

First, we will shortly review some of the local detection techniques that seem to perform well in practice. Among these, one can find robust ``Mahalanobis-type'' detection techniques and a wheighted PCA approach. We suggest an adaptation to one of these to further develop its local characteristic.

Then, examples and simulations, based on linear model of co-regionalisation with Matern models, are reported and discussed in order to compare in an objective way the different detection techniques.