Computing finite mixture estimators in the tails

The finite mixtures regression identifies homogeneous groups within the sample. The data are aggregated into classes sharing similar patterns without any prior knowledge or assumption on the clustering. These clusters are characterized by group-specific regression coefficients to account for between groups heterogeneity. Two different approaches have been independently defined in the literature to compute this estimator not only at the conditional mean but also in the tails. One approach allows the grouping to change according to the selected location/quantile. The other defines the clusters once and for all at the conditional mean, and then moves the regression to the tails, focusing on group specific estimates and allowing between groups comparison of the regression coefficients.