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Mixtures of generalized hyperbolic distributions and mixtures of skew-t distributions for model-based clustering with incomplete data

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  • Wei, Yuhong
  • Tang, Yang
  • McNicholas, Paul D.

Abstract

Robust clustering from incomplete data is an important topic because, in many practical situations, real datasets are heavy-tailed, asymmetric, and/or have arbitrary patterns of missing observations. Flexible methods and algorithms for model-based clustering are presented via mixture of the generalized hyperbolic distributions and its limiting case, the mixture of multivariate skew-t distributions. An analytically feasible EM algorithm is formulated for parameter estimation and imputation of missing values for mixture models employing missing at random mechanisms. The proposed methodologies are investigated through a simulation study with varying proportions of synthetic missing values and illustrated using a real dataset. Comparisons are made with those obtained from the traditional mixture of generalized hyperbolic distribution counterparts by filling in the missing data using the mean imputation method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:130:y:2019:i:c:p:18-41
    DOI: 10.1016/j.csda.2018.08.016
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    2. Cristina Tortora & Brian C. Franczak & Ryan P. Browne & Paul D. McNicholas, 2019. "A Mixture of Coalesced Generalized Hyperbolic Distributions," Journal of Classification, Springer;The Classification Society, vol. 36(1), pages 26-57, April.
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    5. Bhat, Chandra R. & Mondal, Aupal, 2022. "A New Flexible Generalized Heterogeneous Data Model (GHDM) with an Application to Examine the Effect of High Density Neighborhood Living on Bicycling Frequency," Transportation Research Part B: Methodological, Elsevier, vol. 164(C), pages 244-266.

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