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Although there are many papers on variable selection methods based on mean model in the finite mixture of regression models, little work has been done on how to select significant explanatory variables in the modeling of the variance parameter. In this paper, we propose and study a novel class of models: a skew-normal mixture of joint location and scale models to analyze the heteroscedastic skew-normal data coming from a heterogeneous population. 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 is established. Simulation studies are conducted to investigate the finite sample performance of the proposed methodologies. An example is illustrated by the proposed methodologies.

Variable selection for skew-normal mixture of joint location and scale models