Local Statistical Modeling via a Cluster-Weighted Approach with Elliptical Distributions

Cluster-weighted modeling (CWM) is a mixture approach to modeling the joint probability of data coming from a heterogeneous population. Under Gaussian assumptions, we investigate statistical properties of CWM from both theoretical and numerical points of view; in particular, we show that Gaussian CWM includes mixtures of distributions and mixtures of regressions as special cases. Further, we introduce CWM based on Student-{\em t} distributions, which provides a more robust fit for groups of observations with longer than normal tails or noisy data. Theoretical results are illustrated using some empirical studies, considering both simulated and real data. Some generalizations of such models are also outlined.