Finite Mixture at Quantiles and Expectiles

Finite mixture regression identifies homogeneous groups within a sample and computes the regression coefficients in each group. Groups and group coefficients are jointly estimated using an iterative approach. This work extends the finite mixture estimator to the tails of the distribution, by incorporating quantiles and expectiles and relaxing the constraint of constant group probability adopted in previous analysis. The probability of each group depends on the selected location: an observation can be allocated in the best-performing group if we look at low values of the dependent variable, while at higher values it may be assigned to the poorly performing class. We explore two case studies: school data from a PISA math proficiency test and asset returns from the Center for Research in Security Prices. In these real data examples, group classifications change based on the selected location of the dependent variable, and this has an impact on the regression estimates due to the joint computation of class probabilities and class regressions coefficients. A Monte Carlo experiment is conducted to compare the performances of the discussed estimators with results of previous research.