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A mixture of generalized hyperbolic factor analyzers

Author

Listed:
  • Cristina Tortora

    (McMaster University)

  • Paul D. McNicholas

    (McMaster University)

  • Ryan P. Browne

    (McMaster University)

Abstract

The mixture of factor analyzers model, which has been used successfully for the model-based clustering of high-dimensional data, is extended to generalized hyperbolic mixtures. The development of a mixture of generalized hyperbolic factor analyzers is outlined, drawing upon the relationship with the generalized inverse Gaussian distribution. An alternating expectation-conditional maximization algorithm is used for parameter estimation, and the Bayesian information criterion is used to select the number of factors as well as the number of components. The performance of our generalized hyperbolic factor analyzers model is illustrated on real and simulated data, where it performs favourably compared to its Gaussian analogue and other approaches.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:advdac:v:10:y:2016:i:4:d:10.1007_s11634-015-0204-z
    DOI: 10.1007/s11634-015-0204-z
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    Cited by:

    1. Chaofeng Yuan & Wensheng Zhu & Xuming He & Jianhua Guo, 2019. "A mixture factor model with applications to microarray data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 60-76, March.
    2. 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.
    3. 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.
    4. Sharon X. Lee & Tsung-I Lin & Geoffrey J. McLachlan, 2021. "Mixtures of factor analyzers with scale mixtures of fundamental skew normal 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. 15(2), pages 481-512, June.
    5. Nam-Hwui Kim & Ryan Browne, 2019. "Subspace clustering for the finite mixture of generalized hyperbolic 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. 13(3), pages 641-661, September.
    6. Wan-Lun Wang & Luis M. Castro & Yen-Ting Chang & Tsung-I Lin, 2019. "Mixtures of restricted skew-t factor analyzers with common factor loadings," 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. 13(2), pages 445-480, June.
    7. Kim, Nam-Hwui & Browne, Ryan P., 2021. "In the pursuit of sparseness: A new rank-preserving penalty for a finite mixture of factor analyzers," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).
    8. 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).
    9. Paula M. Murray & Ryan P. Browne & Paul D. McNicholas, 2020. "Mixtures of Hidden Truncation Hyperbolic Factor Analyzers," Journal of Classification, Springer;The Classification Society, vol. 37(2), pages 366-379, July.
    10. Petrella, Lea & Raponi, Valentina, 2019. "Joint estimation of conditional quantiles in multivariate linear regression models with an application to financial distress," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 70-84.

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