A parametric regression model by minimum L2 criterion: a study on hydrocarbon pollution of electrical transformers

The purpose of our work 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 unstable. We shall also see how L_2E criterion may be applied in fitting mixture regression models and how it allows to detect clusters of data. Theory is outlined, some examples on simulated data sets are given and an application to data from investigation on risks of fire and electric shocks of electronic transformers is proposed to illustrate the use of the approach. In order to estimate the parameters of the models we implemented some routines in R computing environment.