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Parsimony and parameter estimation for mixtures of multivariate leptokurtic-normal distributions

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Listed:
  • Ryan P. Browne

    (University of Waterloo)

  • Luca Bagnato

    (Catholic University of the Sacred Heart)

  • Antonio Punzo

    (University of Catania)

Abstract

Mixtures of multivariate leptokurtic-normal distributions have been recently introduced in the clustering literature based on mixtures of elliptical heavy-tailed distributions. They have the advantage of having parameters directly related to the moments of practical interest. We derive two estimation procedures for these mixtures. The first one is based on the majorization-minimization algorithm, while the second is based on a fixed point approximation. Moreover, we introduce parsimonious forms of the considered mixtures and we use the illustrated estimation procedures to fit them. We use simulated and real data sets to investigate various aspects of the proposed models and algorithms.

Suggested Citation

  • Ryan P. Browne & Luca Bagnato & Antonio Punzo, 2024. "Parsimony and parameter estimation for mixtures of multivariate leptokurtic-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. 18(3), pages 597-625, September.
    • Handle: RePEc:spr:advdac:v:18:y:2024:i:3:d:10.1007_s11634-023-00558-2
    DOI: 10.1007/s11634-023-00558-2
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    References listed on IDEAS

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    1. Paul D. McNicholas, 2016. "Model-Based Clustering," Journal of Classification, Springer;The Classification Society, vol. 33(3), pages 331-373, October.
    2. repec:bla:biomet:v:71:y:2015:i:4:p:1081-1089 is not listed on IDEAS
    3. Utkarsh J. Dang & Antonio Punzo & Paul D. McNicholas & Salvatore Ingrassia & Ryan P. Browne, 2017. "Multivariate Response and Parsimony for Gaussian Cluster-Weighted Models," Journal of Classification, Springer;The Classification Society, vol. 34(1), pages 4-34, April.
    4. Jian Zhang & Faming Liang, 2010. "Robust Clustering Using Exponential Power Mixtures," Biometrics, The International Biometric Society, vol. 66(4), pages 1078-1086, December.
    5. Matthew Stephens, 2000. "Dealing with label switching in mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 795-809.
    6. Morris, Katherine & Punzo, Antonio & McNicholas, Paul D. & Browne, Ryan P., 2019. "Asymmetric clusters and outliers: Mixtures of multivariate contaminated shifted asymmetric Laplace distributions," Computational Statistics & Data Analysis, Elsevier, vol. 132(C), pages 145-166.
    7. Luca Bagnato & Antonio Punzo & Maria Grazia Zoia, 2022. "Leptokurtic moment-parameterized elliptically contoured distributions with application to financial stock returns," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(2), pages 486-500, January.
    8. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    9. Azzalini, Adelchi & Browne, Ryan P. & Genton, Marc G. & McNicholas, Paul D., 2016. "On nomenclature for, and the relative merits of, two formulations of skew distributions," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 201-206.
    10. Galimberti, Giuliano & Soffritti, Gabriele, 2014. "A multivariate linear regression analysis using finite mixtures of t distributions," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 138-150.
    11. Dankmar Böhning & Ekkehart Dietz & Rainer Schaub & Peter Schlattmann & Bruce Lindsay, 1994. "The distribution of the likelihood ratio for mixtures of densities from the one-parameter exponential family," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(2), pages 373-388, June.
    12. Ryan Browne & Paul McNicholas, 2014. "Estimating common principal components in high dimensions," 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. 8(2), pages 217-226, June.
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