Penalized Maximum Likelihood Estimator for Finite Skew-Laplace-Normal Mixtures

Skew-Laplace-Normal Mixture models is a more flexible framework than the normal mixture models for heterogeneous data with asymmetric behaviors. But it’s likelihood function have some bad math properties, such as the unboundedness of likelihood function and the divergency of skewness parameter, it often mislead statistic inference. In this paper, we given a penalizing the likelihood function method to deal with these problem simultaneously, and we given the detail of proof on parameter have strongly consistency. We also give a modified penalized EM-type algorithms to compute penalized estimators.