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

Author

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  • 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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    9. Jian Zhang & Faming Liang, 2010. "Robust Clustering Using Exponential Power Mixtures," Biometrics, The International Biometric Society, vol. 66(4), pages 1078-1086, December.
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    13. 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.
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