Clusters Detection in Regression Problems: A Similarity Test Between Estimated Models

The purpose of this article is to investigate on the use of the Minimum Integrated Square Error criterion as a practical tool in building useful regression models, notably in all those situations involving the study of large data sets where a substantial number of outliers can be present or data are clustered. We suggest a technique of regression analysis which consists in comparing the results arising from L 2 estimates with the ones obtained applying some common M-estimators. A new index of similarity between functions is proposed and a Monte Carlo test of hypothesis based on it is introduced. Rejecting the hypothesis of similarity between the estimated regression models implies a careful investigation of data structure. Results of a simulation study, referring to several experimental scenarios, are provided to illustrate the approach we propose.