Finite Mixture of Linear Regression Models: An Adaptive Constrained Approach to Maximum Likelihood Estimation

In order to overcome the problems due to the unboundedness of the likelihood, constrained approaches to maximum likelihood estimation in the context of finite mixtures of univariate and multivariate normals have been presented in the literature. One main drawback is that they require a knowledge of the variance and covariance structure.We propose a fully data-driven constrained method for estimation of mixtures of linear regression models. The method does not require any prior knowledge of the variance structure, it is invariant under change of scale in the data and it is easy and ready to implement in standard routines.