A Cluster-Weighted Approach to Local Statistical Modeling

We consider the Cluster Weighted approach in order to model functional dependence between input and output variables based on data coming from an heterogeneous population. Under Gaussian assumptions we investigate some statistical properties of such framework in comparison with some competitive statistical models such as Finite Mixtures of Regression and Finite Mixtures of Regression with Concomitant variables. Further we introduce cluster weighted modeling based on Student-t distributions which provide both more realistic tails for real-world data and robust parametric extension to the fitting of data with respect to the alternative Gaussian models. Theoretical results are illustrated on the ground of some empirical studies, considering both real and simulated data.