Finite mixtures of multivariate skew distributions have become increasingly popular in recent years due to their flexibility and robustness in modeling heterogeneity, asymmetry and leptokurticness of the data. This paper introduces a novel finite mixture of multivariate scale-shape mixtures of skew-normal distributions to enhance strength and flexibility when modeling heterogeneous multivariate data that contain more extreme non-normal features. A computational tractable ECM algorithm which consists of analytically simple E- and CM-steps is developed to carry out maximum likelihood estimation of parameters. The asymptotic covariance matrix of parameter estimates is derived from the observed information matrix using the outer product of expected complete-data scores. We demonstrate the utility of the proposed approach through simulated and real data examples.

中文翻译：

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偏态正态分布的多元尺度混合的有限混合

多元偏斜分布的有限混合近年来变得越来越流行，因为它们在建模数据的异质性、不对称性和高峰态方面具有灵活性和鲁棒性。本文介绍了一种新的斜正态分布的多元尺度形状混合的有限混合，以在对包含更多极端非正态特征的异质多元数据进行建模时增强强度和灵活性。开发了一种由分析简单的 E 和 CM 步骤组成的计算易处理 ECM 算法来执行参数的最大似然估计。参数估计的渐近协方差矩阵是使用预期的完整数据分数的外积从观察到的信息矩阵得出的。