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Robust model-based clustering via mixtures of skew-t distributions with missing information

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  • Wan-Lun Wang
  • Tsung-I Lin

Abstract

Multivariate mixture modeling approach using the skew-t distribution has emerged as a powerful and flexible tool for robust model-based clustering. The occurrence of missing data is a ubiquitous problem in almost every scientific field. In this paper, we offer a computationally flexible EM-type procedure for learning multivariate skew-t mixture models to deal with missing data under missing at random mechanisms. Further, we present an information-based approach to approximating the asymptotic covariance matrix of the maximum likelihood estimators using the outer product of the scores. To assist the development and ease the implementation of our algorithm, two auxiliary permutation matrices are utilized for fast determination of the observed and missing parts of each observation. The practical usefulness of the proposed methodology is illustrated through simulations with varying proportions of artificial missing values and a real data example with genuine missing values. Copyright Springer-Verlag Berlin Heidelberg 2015

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  • Wan-Lun Wang & Tsung-I Lin, 2015. "Robust model-based clustering via mixtures of skew-t distributions with missing information," 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. 9(4), pages 423-445, December.
    • Handle: RePEc:spr:advdac:v:9:y:2015:i:4:p:423-445
    DOI: 10.1007/s11634-015-0221-y
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    Cited by:

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    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. Sahin, Özge & Czado, Claudia, 2022. "Vine copula mixture models and clustering for non-Gaussian data," Econometrics and Statistics, Elsevier, vol. 22(C), pages 136-158.
    4. Wan-Lun Wang & Tsung-I Lin, 2020. "Automated learning of mixtures of factor analysis models with missing information," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 1098-1124, December.
    5. Lachos, Víctor H. & Moreno, Edgar J. López & Chen, Kun & Cabral, Celso Rômulo Barbosa, 2017. "Finite mixture modeling of censored data using the multivariate Student-t distribution," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 151-167.
    6. Reyhaneh Rikhtehgaran & Iraj Kazemi, 2016. "The determination of uncertainty levels in robust clustering of subjects with longitudinal observations using the Dirichlet process mixture," 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 541-562, December.
    7. Francisco H. C. Alencar & Larissa A Matos & Víctor H. Lachos, 2022. "Finite Mixture of Censored Linear Mixed Models for Irregularly Observed Longitudinal Data," Journal of Classification, Springer;The Classification Society, vol. 39(3), pages 463-486, November.

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