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Estimation and order selection for multivariate exponential power mixture models

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  • Chen, Xiao
  • Feng, Zhenghui
  • Peng, Heng

Abstract

Finite mixture model is a promising statistical model in investigating the heterogeneity of population. For multivariate non-Gaussian density estimation and approximation, in this paper, we consider to use multivariate exponential power mixture models. We propose the penalized-likelihood method with a generalized EM algorithm to estimate locations, scale matrices, shape parameters, and mixing probabilities. Order selection is achieved simultaneously. Properties of the estimated order have been derived. Although we mainly focus on the unconstrained scale matrix type in multivariate exponential power mixture models, three more parsimonious types of scale matrix have also been considered. Performance based on simulation and real data analysis implies the parsimony of the exponential power mixture models, and verifies the consistency of order selection.

Suggested Citation

  • Chen, Xiao & Feng, Zhenghui & Peng, Heng, 2023. "Estimation and order selection for multivariate exponential power mixture models," Journal of Multivariate Analysis, Elsevier, vol. 195(C).
    • Handle: RePEc:eee:jmvana:v:195:y:2023:i:c:s0047259x22001312
    DOI: 10.1016/j.jmva.2022.105140
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    References listed on IDEAS

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    1. Utkarsh J. Dang & Ryan P. Browne & Paul D. McNicholas, 2015. "Mixtures of multivariate power exponential distributions," Biometrics, The International Biometric Society, vol. 71(4), pages 1081-1089, December.
    2. Victor Korolev, 2020. "Some Properties of Univariate and Multivariate Exponential Power Distributions and Related Topics," Mathematics, MDPI, vol. 8(11), pages 1-27, November.
    3. Gómez-Sánchez-Manzano, E. & Gómez-Villegas, M.A. & Marín, J.M., 2006. "Sequences of elliptical distributions and mixtures of normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 295-310, February.
    4. Antoni Bosch-Domènech & José Montalvo & Rosemarie Nagel & Albert Satorra, 2010. "A finite mixture analysis of beauty-contest data using generalized beta distributions," Experimental Economics, Springer;Economic Science Association, vol. 13(4), pages 461-475, December.
    5. Jian Zhang & Faming Liang, 2010. "Robust Clustering Using Exponential Power Mixtures," Biometrics, The International Biometric Society, vol. 66(4), pages 1078-1086, December.
    6. Szekely, Gábor J. & Rizzo, Maria L., 2005. "A new test for multivariate normality," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 58-80, March.
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