Unsupervised Liu-type Shrinkage Estimators for Mixture of Regression Models

In many applications (e.g., medical studies), the population of interest (e.g., disease status) comprises heterogeneous subpopulations. The mixture of probabilistic regression models is one of the most common techniques to incorporate the information of covariates into learning of the population heterogeneity. Despite its flexibility, the model may lead to unreliable estimates in the presence of multicollinearity problem. In this paper, we develop Liu-type shrinkage methods through an unsupervised learning approach to estimate the model coefficients in multicollinearity. The performance of the developed methods is evaluated via classification and stochastic versions of EM algorithms. The numerical studies show that the proposed methods outperform their Ridge and maximum likelihood counterparts. Finally, the developed methods are applied to analyze the bone mineral data of women aged 50 and older.