IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v195y2023ics0047259x22001312.html
   My bibliography  Save this article

Estimation and order selection for multivariate exponential power mixture models

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X22001312
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2022.105140?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. 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.
    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. John Lawrence, 2023. "Moments of the Noncentral Chi Distribution," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1243-1259, August.
    2. Gábor J. Székely & Maria L. Rizzo, 2020. "Comments on: Tests for multivariate normality—a critical review with emphasis on weighted $$L^{2}$$ L 2 -statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 907-910, December.
    3. Mariano Runco, 2013. "Estimating depth of reasoning in a repeated guessing game with no feedback," Experimental Economics, Springer;Economic Science Association, vol. 16(3), pages 402-413, September.
    4. Carlo A. Favero & Alessandro Melone, 2019. "Asset Pricing vs Asset Expected Returning in Factor Models," Working Papers 651, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    5. Timo Ehrig & Jaison Manjaly & Aditya Singh & Shyam Sunder, 2022. "Adaptive Rationality in Strategic Interaction: Do Emotions Regulate Thinking About Others?," Strategy Science, INFORMS, vol. 7(4), pages 330-349, December.
    6. M. Dolores Jiménez-Gamero, 2020. "Comments on: Tests for multivariate normality—a critical review with emphasis on weighted $$L^2$$ L 2 -statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 893-897, December.
    7. Constandina Koki & Loukia Meligkotsidou & Ioannis Vrontos, 2020. "Forecasting under model uncertainty: Non‐homogeneous hidden Markov models with Pòlya‐Gamma data augmentation," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(4), pages 580-598, July.
    8. 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.
    9. Norbert Henze & María Dolores Jiménez-Gamero, 2019. "A new class of tests for multinormality with i.i.d. and garch data based on the empirical moment generating function," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 499-521, June.
    10. Hanaki, Nobuyuki & Koriyama, Yukio & Sutan, Angela & Willinger, Marc, 2019. "The strategic environment effect in beauty contest games," Games and Economic Behavior, Elsevier, vol. 113(C), pages 587-610.
    11. Nagel, Rosemarie & Bühren, Christoph & Frank, Björn, 2017. "Inspired and inspiring: Hervé Moulin and the discovery of the beauty contest game," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 191-207.
    12. Philip Dörr & Bruno Ebner & Norbert Henze, 2021. "Testing multivariate normality by zeros of the harmonic oscillator in characteristic function spaces," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 456-501, June.
    13. Quessy, Jean-François, 2021. "A Szekely–Rizzo inequality for testing general copula homogeneity hypotheses," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    14. Tenreiro, Carlos, 2011. "An affine invariant multiple test procedure for assessing multivariate normality," Computational Statistics & Data Analysis, Elsevier, vol. 55(5), pages 1980-1992, May.
    15. Florian Ziel & Kevin Berk, 2019. "Multivariate Forecasting Evaluation: On Sensitive and Strictly Proper Scoring Rules," Papers 1910.07325, arXiv.org.
    16. Philip Dörr & Bruno Ebner & Norbert Henze, 2021. "A new test of multivariate normality by a double estimation in a characterizing PDE," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(3), pages 401-427, April.
    17. Jun Li & Yao Yu, 2015. "A Nonparametric Test of Missing Completely at Random for Incomplete Multivariate Data," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 707-726, September.
    18. Engel, Christoph, 2020. "Estimating heterogeneous reactions to experimental treatments," Journal of Economic Behavior & Organization, Elsevier, vol. 178(C), pages 124-147.
    19. Ravi Kashyap, 2016. "The Perfect Marriage and Much More: Combining Dimension Reduction, Distance Measures and Covariance," Papers 1603.09060, arXiv.org, revised Jul 2019.
    20. Tomasz Górecki & Lajos Horváth & Piotr Kokoszka, 2020. "Tests of Normality of Functional Data," International Statistical Review, International Statistical Institute, vol. 88(3), pages 677-697, December.

    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:eee:jmvana:v:195:y:2023:i:c:s0047259x22001312. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.