Finite mixtures of canonical fundamental skew t-distributions: The unification of the restricted and unrestricted skew t-mixture models

Lee, Sharon X and McLachlan, Geoffrey J (2016) Finite mixtures of canonical fundamental skew t-distributions: The unification of the restricted and unrestricted skew t-mixture models. Statistics and Computing, 26 3: 573-589. doi:10.1007/s11222-015-9545-x


Author Lee, Sharon X
McLachlan, Geoffrey J
Title Finite mixtures of canonical fundamental skew t-distributions: The unification of the restricted and unrestricted skew t-mixture models
Journal name Statistics and Computing   Check publisher's open access policy
ISSN 0960-3174
1573-1375
Publication date 2016-05
Year available 2015
Sub-type Article (original research)
DOI 10.1007/s11222-015-9545-x
Open Access Status Not Open Access
Volume 26
Issue 3
Start page 573
End page 589
Total pages 17
Place of publication New York, United States
Publisher Springer New York LLC
Collection year 2016
Language eng
Formatted abstract
This paper introduces a finite mixture of canonical fundamental skew t (CFUST) distributions for a model-based approach to clustering where the clusters are asymmetric and possibly long-tailed (in: Lee and McLachlan, arXiv:​1401.​8182 [statME], 2014b). The family of CFUST distributions includes the restricted multivariate skew t and unrestricted multivariate skew t distributions as special cases. In recent years, a few versions of the multivariate skew t (MST) mixture model have been put forward, together with various EM-type algorithms for parameter estimation. These formulations adopted either a restricted or unrestricted characterization for their MST densities. In this paper, we examine a natural generalization of these developments, employing the CFUST distribution as the parametric family for the component distributions, and point out that the restricted and unrestricted characterizations can be unified under this general formulation. We show that an exact implementation of the EM algorithm can be achieved for the CFUST distribution and mixtures of this distribution, and present some new analytical results for a conditional expectation involved in the E-step.
Keyword Mixture models
EM algorithm
Skew normal distributions
Skew t distributions
Fundamental skew distributions
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ
Additional Notes Published online 28 February 2015

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2016 Collection
 
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