Clusters Detection in Regression Models Applied to a Pollution Risk Evaluation Problem. The L_2 Approach.

Purpose of this paper is to investigate on the use of L_2 distance as a theoretical and practical estimation tool for parametric regression models. This approach is particularly helpful in all those situations involving the study of large data sets, handling large samples with a consistent numbers of outliers, situations in which maximum likelihood regression models are usually unstable. We shall also see how L_2 criterion may be applied in fitting mixture regression models and how it allows to detect clusters of data. After explaining the use of the methods with some simulated examples, we shall point out main results of an industrial case study.