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A mixture of SDB skew-t factor analyzers

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  • Murray, Paula M.
  • Browne, Ryan P.
  • McNicholas, Paul D.

Abstract

Mixtures of skew-t distributions offer a flexible choice for model-based clustering. A mixture model of this sort can be implemented using a variety of formulations of the skew-t distribution. A mixture of skew-t factor analyzers model for clustering of high-dimensional data using a flexible formulation of the skew-t distribution is developed. Methodological details of the proposed approach, which represents an extension of the mixture of factor analyzers model to a flexible skew-t distribution, are outlined and details of parameter estimation are provided. Clustering results are illustrated and compared to an alternative formulation of the mixture of skew-t factor analyzers model as well as the mixture of factor analyzers model.

Suggested Citation

  • Murray, Paula M. & Browne, Ryan P. & McNicholas, Paul D., 2017. "A mixture of SDB skew-t factor analyzers," Econometrics and Statistics, Elsevier, vol. 3(C), pages 160-168.
    • Handle: RePEc:eee:ecosta:v:3:y:2017:i:c:p:160-168
    DOI: 10.1016/j.ecosta.2017.05.001
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    References listed on IDEAS

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    1. Vrbik, I. & McNicholas, P.D., 2012. "Analytic calculations for the EM algorithm for multivariate skew-t mixture models," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1169-1174.
    2. Bouveyron, Charles & Brunet-Saumard, Camille, 2014. "Model-based clustering of high-dimensional data: A review," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 52-78.
    3. Paul D. McNicholas, 2016. "Model-Based Clustering," Journal of Classification, Springer;The Classification Society, vol. 33(3), pages 331-373, October.
    4. Murray, Paula M. & Browne, Ryan P. & McNicholas, Paul D., 2014. "Mixtures of skew-t factor analyzers," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 326-335.
    5. McLachlan, Geoffrey J. & Lee, Sharon X., 2016. "Comment on “On nomenclature, and the relative merits of two formulations of skew distributions” by A. Azzalini, R. Browne, M. Genton, and P. McNicholas," Statistics & Probability Letters, Elsevier, vol. 116(C), pages 1-5.
    6. Sanjeena Subedi & Paul McNicholas, 2014. "Variational Bayes approximations for clustering via mixtures of normal inverse Gaussian distributions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(2), pages 167-193, June.
    7. Lin, Tsung-I & McLachlan, Geoffrey J. & Lee, Sharon X., 2016. "Extending mixtures of factor models using the restricted multivariate skew-normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 398-413.
    8. Cristina Tortora & Paul D. McNicholas & Ryan P. Browne, 2016. "A mixture of generalized hyperbolic factor analyzers," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 10(4), pages 423-440, December.
    9. Wraith, Darren & Forbes, Florence, 2015. "Location and scale mixtures of Gaussians with flexible tail behaviour: Properties, inference and application to multivariate clustering," Computational Statistics & Data Analysis, Elsevier, vol. 90(C), pages 61-73.
    10. Andrews, Jeffrey L. & McNicholas, Paul D. & Subedi, Sanjeena, 2011. "Model-based classification via mixtures of multivariate t-distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 520-529, January.
    11. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    12. Azzalini, Adelchi & Browne, Ryan P. & Genton, Marc G. & McNicholas, Paul D., 2016. "On nomenclature for, and the relative merits of, two formulations of skew distributions," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 201-206.
    13. Angela Montanari & Cinzia Viroli, 2010. "A skew-normal factor model for the analysis of student satisfaction towards university courses," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(3), pages 473-487.
    14. Morris, Katherine & McNicholas, Paul D., 2016. "Clustering, classification, discriminant analysis, and dimension reduction via generalized hyperbolic mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 97(C), pages 133-150.
    15. Tsung-I Lin & Pal Wu & Geoffrey McLachlan & Sharon Lee, 2015. "A robust factor analysis model using the restricted skew- $$t$$ t distribution," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 510-531, September.
    16. Arellano-Valle, Reinaldo B. & Genton, Marc G., 2005. "On fundamental skew distributions," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 93-116, September.
    17. Dankmar Böhning & Ekkehart Dietz & Rainer Schaub & Peter Schlattmann & Bruce Lindsay, 1994. "The distribution of the likelihood ratio for mixtures of densities from the one-parameter exponential family," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(2), pages 373-388, June.
    18. McLachlan, G.J. & Bean, R.W. & Ben-Tovim Jones, L., 2007. "Extension of the mixture of factor analyzers model to incorporate the multivariate t-distribution," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5327-5338, July.
    19. O’Hagan, Adrian & Murphy, Thomas Brendan & Gormley, Isobel Claire & McNicholas, Paul D. & Karlis, Dimitris, 2016. "Clustering with the multivariate normal inverse Gaussian distribution," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 18-30.
    20. Vrbik, Irene & McNicholas, Paul D., 2014. "Parsimonious skew mixture models for model-based clustering and classification," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 196-210.
    21. McNicholas, P.D. & Murphy, T.B. & McDaid, A.F. & Frost, D., 2010. "Serial and parallel implementations of model-based clustering via parsimonious Gaussian mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 54(3), pages 711-723, March.
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    3. Wei, Yuhong & Tang, Yang & McNicholas, Paul D., 2019. "Mixtures of generalized hyperbolic distributions and mixtures of skew-t distributions for model-based clustering with incomplete data," Computational Statistics & Data Analysis, Elsevier, vol. 130(C), pages 18-41.
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    6. Lee, Sharon X. & McLachlan, Geoffrey J., 2021. "On formulations of skew factor models: Skew factors and/or skew errors," Statistics & Probability Letters, Elsevier, vol. 168(C).
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    9. Wan-Lun Wang & Tsung-I Lin, 2022. "Robust clustering of multiply censored data via mixtures of t factor analyzers," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 22-53, March.

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