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A constrained maximum likelihood estimation for skew normal mixtures
Metrika ( IF 0.7 ) Pub Date : 2022-06-30 , DOI: 10.1007/s00184-022-00873-2
Libin Jin, Sung Nok Chiu, Jianhua Zhao, Lixing Zhu

For a finite mixture of skew normal distributions, the maximum likelihood estimator is not well-defined because of the unboundedness of the likelihood function when scale parameters go to zero and the divergency of the skewness parameter estimates. To overcome these two problems simultaneously, we propose constrained maximum likelihood estimators under constraints on both the scale parameters and the skewness parameters. The proposed estimators are consistent and asymptotically efficient under relaxed constraints on the scale and skewness parameters. Numerical simulations show that in finite sample cases the proposed estimators outperform the ordinary maximum likelihood estimators. Two real datasets are used to illustrate the success of the proposed approach.



中文翻译:

偏斜正态混合的约束最大似然估计

对于偏态正态分布的有限混合,最大似然估计量没有明确定义,因为当尺度参数变为零时似然函数的无界性和偏态参数估计的发散性。为了同时克服这两个问题,我们提出了在尺度参数和偏度参数约束下的约束最大似然估计器。所提出的估计量在尺度和偏度参数的宽松约束下是一致的且渐近有效的。数值模拟表明,在有限样本情况下,所提出的估计器优于普通的最大似然估计器。两个真实的数据集用于说明所提出方法的成功。

更新日期:2022-07-01
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