Clusters Detection in Regression Problems: the Integrated Square Error Approach

Purpose of this paper is to investigate on the use of the IntegratedSquare Error as a practical tool in building useful regression models, notably inall 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 L2 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 estimatedregression models implies a careful investigation of data structure. Resultsof a simulation study, referring to several experimental scenarios, are provided toillustrate the approach we propose.