IDEAS home Printed from https://ideas.repec.org/a/spr/advdac/v18y2024i3d10.1007_s11634-023-00558-2.html
   My bibliography  Save this article

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

Author

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11634-023-00558-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11634-023-00558-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. repec:bla:biomet:v:71:y:2015:i:4:p:1081-1089 is not listed on IDEAS
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Paul D. McNicholas, 2016. "Model-Based Clustering," Journal of Classification, Springer;The Classification Society, vol. 33(3), pages 331-373, October.
    8. Jian Zhang & Faming Liang, 2010. "Robust Clustering Using Exponential Power Mixtures," Biometrics, The International Biometric Society, vol. 66(4), pages 1078-1086, December.
    9. 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.
    10. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    11. 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.
    12. Francesca Greselin & Salvatore Ingrassia & Antonio Punzo, 2011. "Assessing the pattern of covariance matrices via an augmentation multiple testing procedure," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 20(2), pages 141-170, June.
    13. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sanjeena Subedi & Paul D. McNicholas, 2021. "A Variational Approximations-DIC Rubric for Parameter Estimation and Mixture Model Selection Within a Family Setting," Journal of Classification, Springer;The Classification Society, vol. 38(1), pages 89-108, April.
    2. Cristina Tortora & Brian C. Franczak & Ryan P. Browne & Paul D. McNicholas, 2019. "A Mixture of Coalesced Generalized Hyperbolic Distributions," Journal of Classification, Springer;The Classification Society, vol. 36(1), pages 26-57, April.
    3. 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.
    4. 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.
    5. Antonio Punzo & Paul. D. McNicholas, 2017. "Robust Clustering in Regression Analysis via the Contaminated Gaussian Cluster-Weighted Model," Journal of Classification, Springer;The Classification Society, vol. 34(2), pages 249-293, July.
    6. Alessio Farcomeni & Antonio Punzo, 2020. "Robust model-based clustering with mild and gross outliers," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 989-1007, December.
    7. Murray, Paula M. & Browne, Ryan P. & McNicholas, Paul D., 2017. "A mixture of SDB skew-t factor analyzers," Econometrics and Statistics, Elsevier, vol. 3(C), pages 160-168.
    8. Angelo Mazza & Antonio Punzo, 2020. "Mixtures of multivariate contaminated normal regression models," Statistical Papers, Springer, vol. 61(2), pages 787-822, April.
    9. Yuan Fang & Dimitris Karlis & Sanjeena Subedi, 2022. "Infinite Mixtures of Multivariate Normal-Inverse Gaussian Distributions for Clustering of Skewed Data," Journal of Classification, Springer;The Classification Society, vol. 39(3), pages 510-552, November.
    10. 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).
    11. Tang, Yang & Browne, Ryan P. & McNicholas, Paul D., 2015. "Model based clustering of high-dimensional binary data," Computational Statistics & Data Analysis, Elsevier, vol. 87(C), pages 84-101.
    12. Salvatore D. Tomarchio & Paul D. McNicholas & Antonio Punzo, 2021. "Matrix Normal Cluster-Weighted Models," Journal of Classification, Springer;The Classification Society, vol. 38(3), pages 556-575, October.
    13. 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.
    14. Sharon M. McNicholas & Paul D. McNicholas & Daniel A. Ashlock, 2021. "An Evolutionary Algorithm with Crossover and Mutation for Model-Based Clustering," Journal of Classification, Springer;The Classification Society, vol. 38(2), pages 264-279, July.
    15. Jason Hou-Liu & Ryan P. Browne, 2022. "Factor and hybrid components for model-based clustering," 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(2), pages 373-398, June.
    16. Wan-Lun Wang & Yu-Chen Yang & Tsung-I Lin, 2024. "Extending finite mixtures of nonlinear mixed-effects models with covariate-dependent mixing weights," 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(2), pages 271-307, June.
    17. Sugasawa, Shonosuke & Kobayashi, Genya, 2022. "Robust fitting of mixture models using weighted complete estimating equations," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    18. Hung Tong & Cristina Tortora, 2024. "Missing Values and Directional Outlier Detection in Model-Based Clustering," Journal of Classification, Springer;The Classification Society, vol. 41(3), pages 480-513, November.
    19. Naderi, Mehrdad & Mirfarah, Elham & Wang, Wan-Lun & Lin, Tsung-I, 2023. "Robust mixture regression modeling based on the normal mean-variance mixture distributions," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    20. Sangkon Oh & Byungtae Seo, 2023. "Merging Components in Linear Gaussian Cluster-Weighted Models," Journal of Classification, Springer;The Classification Society, vol. 40(1), pages 25-51, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:advdac:v:18:y:2024:i:3:d:10.1007_s11634-023-00558-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.