Unsupervised Liu-type shrinkage estimators for mixture of regression models.

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, unreliable estimates can occur due to multicollinearity among covariates. In this paper, we develop Liu-type shrinkage methods through an unsupervised learning approach to estimate the model coefficients in the presence of multicollinearity. We evaluate the performance of our proposed methods via classification and stochastic versions of the expectation-maximization algorithm. We show using numerical simulations that the proposed methods outperform their Ridge and maximum likelihood counterparts. Finally, we apply our methods to analyze the bone mineral data of women aged 50 and older.