Finite mixtures of canonical fundamental skew $$t$$t-distributions

This paper introduces a finite mixture of canonical fundamental skew $$t$$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 $$t$$t and unrestricted multivariate skew $$t$$t distributions as special cases. In recent years, a few versions of the multivariate skew $$t$$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.

• Publication year

  2014

• Venue

  Statistics and computing

• Publication date

  2014-05-04

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1007/s11222-015-9545-xarXiv 1405.0685
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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