Finite mixtures of multivariate skew t-distributions: Some recent and new results

Lee, Sharon and McLachlan, Geoffrey J. (2014) Finite mixtures of multivariate skew t-distributions: Some recent and new results. Statistics and Computing, 24 2: 181-202. doi:10.1007/s11222-012-9362-4


Author Lee, Sharon
McLachlan, Geoffrey J.
Title Finite mixtures of multivariate skew t-distributions: Some recent and new results
Journal name Statistics and Computing   Check publisher's open access policy
ISSN 0960-3174
1573-1375
Publication date 2014-03
Year available 2012
Sub-type Article (original research)
DOI 10.1007/s11222-012-9362-4
Open Access Status
Volume 24
Issue 2
Start page 181
End page 202
Total pages 22
Place of publication New York, United States
Publisher Springer New York LLC
Collection year 2014
Language eng
Formatted abstract
Finite mixtures of multivariate skew t (MST) distributions have proven to be useful in modelling heterogeneous data with asymmetric and heavy tail behaviour. Recently, they have been exploited as an effective tool for modelling flow cytometric data. A number of algorithms for the computation of the maximum likelihood (ML) estimates for the model parameters of mixtures of MST distributions have been put forward in recent years. These implementations use various characterizations of the MST distribution, which are similar but not identical. While exact implementation of the expectation-maximization (EM) algorithm can be achieved for 'restricted' characterizations of the component skew t-distributions, Monte Carlo (MC) methods have been used to fit the 'unrestricted' models. In this paper, we review several recent fitting algorithms for finite mixtures of multivariate skew t-distributions, at the same time clarifying some of the connections between the various existing proposals. In particular, recent results have shown that the EM algorithm can be implemented exactly for faster computation of ML estimates for mixtures with unrestricted MST components. The gain in computational time is effected by noting that the semi-infinite integrals on the E-step of the EM algorithm can be put in the form of moments of the truncated multivariate non-central t-distribution, similar to the restricted case, which subsequently can be expressed in terms of the non-truncated form of the central t-distribution function for which fast algorithms are available. We present comparisons to illustrate the relative performance of the restricted and unrestricted models, and demonstrate the usefulness of the recently proposed methodology for the unrestricted MST mixture, by some applications to three real datasets.
Keyword EM algorithm
Mixture models
Skew normal distributions
Skew t component distributions
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2015 Collection
 
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