Penalized maximum likelihood estimation for skew normal mixtures
Zhu Lixing, Zhu Liping, Xu Wangli, Libin Jin · Scientia Sinica Mathematica · 2019
Skew normal mixture models provide a more flexible frameworkthan the popular normal mixtures for modelling heterogeneous datawith asymmetric behaviors. Due to the unboundedness of likelihoodfunction and the divergency of shape parameters, the maximum likelihoodestimators of the parameters of interest are often not well defined, leading to dissatisfactory inferential process.We put forward a proposal to deal with these issues simultaneouslyin the context of penalizing likelihood function.The resulting penalized maximum likelihood estimator is proved to be strongly consistent when the putative order of mixture is equal toor greater than the true one. We also provide penalized EM-type algorithms to compute penalized estimators. Finite sample performances are examined bysimulations and the comparison to the existing methods.Two real examples including the famous Iris dataset are analysed for illustration.