Statistical algorithms for Cluster Weighted Models

Cluster-weighted modeling (CWM) is a mixture approach to modeling the joint probability of data coming from a heterogeneous population. In this thesis first we investigate statistical properties of CWM from both theoretical and numerical point of view for both Gaussian and Student-t CWM. Then we introduce a novel family of twelve mixture models, all nested in the linear-t cluster weighted model (CWM). This family of models provides a unified framework that also includes the linear Gaussian CWM as a special case. Parameters estimation is carried out through algorithms based on maximum likelihood estimation and both the BIC and ICL are used for model selection. Finally, based on these algorithms, a software package for the R language has been implemented.