Estimation and variable selection for mixture of joint mean and variance models

Mixture of regression models are one of the most important statistical data analysis tools in a heterogeneous population. Similar to modeling variance parameter in a homogeneous population, we apply the idea of joint mean and variance models to the mixture of regression models and propose a new class of models: mixture of joint mean and variance models to analyze the heteroscedastic normal data coming from a heterogeneous population in this paper. The problem of variable selection for the proposed models is considered. In particular, a modified Expectation-Maximization (EM) algorithm for estimating the model parameters is developed. The consistency and the oracle property of the penalized estimators are established. Properties of the estimators of the regression coefficients are evaluated through Monte Carlo simulations. Finally, a real data analysis is illustrated by the proposed methodologies.