Finite mixtures of multivariate scale-shape mixtures of skew-normal distributions
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Finite mixtures of multivariate scale-shape mixtures of skew-normal distributions Wan-Lun Wang1 · Ahad Jamalizadeh2,3 · Tsung-I Lin4,5 Received: 3 May 2018 / Revised: 24 September 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018
Abstract 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. Keywords Asymmetry · ECM algorithm · Robustness · Shape mixtures · Truncated normal Mathematics Subject Classification 62H12 · 62H30
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00362018-01061-z) contains supplementary material, which is available to authorized users.
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Tsung-I Lin [email protected]
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Department of Statistics, Graduate Institute of Statistics and Actuarial Science, Feng Chia University, Taichung 40724, Taiwan
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Department of Statistics, Faculty of Mathematics & Computer, Shahid Bahonar University of Kerman, Kerman, Iran
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Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman, Iran
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Institute of Statistics, National Chung Hsing University, Taichung 402, Taiwan
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Department of Public Health, China Medical University, Taichung 404, Taiwan
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W.-L. Wang et al.
1 Introduction Finite mixtures of multivariate skew distributions have attracted considerable attention and been shown to successfully solve many practical problems due to their tremendous flexibility in modeling heterogeneous data with multimodality, skewness and possible heavy tails simultaneously. The most notable proposals include the mixture of multivariate skew-normal (MSN) distributions (Lin 2009) and that of multivariate skew-t (MST) distributions (Lin 2010), and both of which were extended by several authors, see, for example, the mixture of skew-normal/independent (SNI) distributions (Cabral et al. 2012), the mixture of skew-t-normal (STN) distributions (Lin et al. 2014), and the mixture of canonical fundamental skew-t (CFUST) distributions (Lee and McLachlan 2016), among others. It is interesting to note that the SNI family can be viewed as a special case of the scale mixtures of SN variates put forward by Branco and Dey (2001), and the CFUST distribution is a member of the class of canonical fundamental skew symmetric (CFUSS) distribut
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