偏正态混合模型的惩罚极大似然估计

在分析具有异质性和非对称性数据时，偏正态混合模型提供一种比经典的Gauss混合模型更为灵活的建模方式。然而，由于无界的似然函数和发散的形状参数，该模型的极大似然估计并未被正确定义，进一步导致不理想的推断过程。为同时解决这两个问题，本文基于惩罚似然提出一种新的估计方案，并证明在混合分布的类别个数大于或等于真实的类别个数时，相应的惩罚极大似然估计是强相合的。同时，本文也提出相应的惩罚EM (expectation maximization)算法来计算惩罚估计。最后，通过模拟分析与现有方法比较研究估计方法在有限样本下的表现，并采用两个实例说明方法的有效性。

Skew normal mixture models provide a more flexible framework than the popular normal mixtures for modelling heterogeneous data with asymmetric behaviors. Due to the unboundedness of likelihood function and the divergency of shape parameters, the maximum likelihood estimators 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 simultaneously in 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 to or greater than the true one. We also provide penalized EM-type algorithms to compute penalized estimators. Finite sample performances are examined by simulations and the comparison to the existing methods.Two real examples including the famous Iris dataset are analysed for illustration.