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Maximum likelihood inference for the multivariate t mixture model

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  • Wang, Wan-Lun
  • Lin, Tsung-I

Abstract

Multivariate t mixture (TMIX) models have emerged as a powerful tool for robust modeling and clustering of heterogeneous continuous multivariate data with observations containing longer than normal tails or atypical observations. In this paper, we explicitly derive the score vector and Hessian matrix of TMIX models to approximate the information matrix under the general and three special cases. As a result, the standard errors of maximum likelihood (ML) estimators are calculated using the outer-score, Hessian matrix, and sandwich-type methods. We have also established some asymptotic properties under certain regularity conditions. The utility of the new theory is illustrated with the analysis of real and simulated data sets.

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  • Wang, Wan-Lun & Lin, Tsung-I, 2016. "Maximum likelihood inference for the multivariate t mixture model," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 54-64.
    • Handle: RePEc:eee:jmvana:v:149:y:2016:i:c:p:54-64
    DOI: 10.1016/j.jmva.2016.03.009
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    5. Lin, Tsung-I, 2014. "Learning from incomplete data via parameterized t mixture models through eigenvalue decomposition," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 183-195.
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    Cited by:

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    2. 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.
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    4. Bartolucci, Francesco & Bacci, Silvia & Pigini, Claudia, 2017. "Misspecification test for random effects in generalized linear finite-mixture models for clustered binary and ordered data," Econometrics and Statistics, Elsevier, vol. 3(C), pages 112-131.
    5. Dirick, Lore & Claeskens, Gerda & Vasnev, Andrey & Baesens, Bart, 2022. "A hierarchical mixture cure model with unobserved heterogeneity for credit risk," Econometrics and Statistics, Elsevier, vol. 22(C), pages 39-55.
    6. Diani, Cecilia & Galimberti, Giuliano & Soffritti, Gabriele, 2022. "Multivariate cluster-weighted models based on seemingly unrelated linear regression," Computational Statistics & Data Analysis, Elsevier, vol. 171(C).
    7. Murray, Paula M. & Browne, Ryan P. & McNicholas, Paul D., 2017. "Hidden truncation hyperbolic distributions, finite mixtures thereof, and their application for clustering," Journal of Multivariate Analysis, Elsevier, vol. 161(C), pages 141-156.
    8. Wan-Lun Wang & Tsung-I Lin, 2022. "Robust clustering via mixtures of t factor analyzers with incomplete data," 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. 16(3), pages 659-690, September.

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