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Bayesian local bandwidths in a flexible semiparametric kernel estimation for multivariate count data with diagnostics

Author

Listed:
  • Sobom M. Somé

    (Université Thomas SANKARA
    Université Joseph KI-ZERBO)

  • Célestin C. Kokonendji

    (Université de Franche-Comté
    Université de Bangui)

  • Nawel Belaid

    (University of Bejaia)

  • Smail Adjabi

    (University of Bejaia)

  • Rahma Abid

    (University of Sfax, Sfax, Tunisia and University Paris-Dauphine Tunis)

Abstract

In this paper, we consider a flexible semiparametric approach for estimating multivariate probability mass functions. The corresponding estimator is governed by a parametric starter, for instance a multivariate Poisson distribution with nonnegative cross correlations which is basically estimated through an expectation–maximization algorithm, and a nonparametric part which is an unknown weight discrete function to be smoothed through multiple binomial kernels. Our central focus is upon the selection matrix of bandwidths by the local Bayesian method. We additionally discuss the diagnostic model to enact an appropriate choice between the parametric, semiparametric and nonparametric approaches. Retaining a pure nonparametric method implies losing parametric benefices in this modelling framework. Practical applications, including a tail probability estimation, on multivariate count datasets are analyzed under several scenarios of correlations and dispersions. This semiparametic approach demonstrates superior performances and better interpretations compared to parametric and nonparametric ones.

Suggested Citation

  • Sobom M. Somé & Célestin C. Kokonendji & Nawel Belaid & Smail Adjabi & Rahma Abid, 2023. "Bayesian local bandwidths in a flexible semiparametric kernel estimation for multivariate count data with diagnostics," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(3), pages 843-865, September.
    • Handle: RePEc:spr:stmapp:v:32:y:2023:i:3:d:10.1007_s10260-023-00682-5
    DOI: 10.1007/s10260-023-00682-5
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    References listed on IDEAS

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    1. Dimitris Karlis, 2003. "An EM algorithm for multivariate Poisson distribution and related models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(1), pages 63-77.
    2. Bent Jørgensen & Célestin Kokonendji, 2016. "Discrete dispersion models and their Tweedie asymptotics," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(1), pages 43-78, January.
    3. Lynda Harfouche & Smail Adjabi & Nabil Zougab & Benedikt Funke, 2018. "Multiplicative bias correction for discrete kernels," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(2), pages 253-276, June.
    4. Karlis, Dimitris & Ntzoufras, Ioannis, 2005. "Bivariate Poisson and Diagonal Inflated Bivariate Poisson Regression Models in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 14(i10).
    5. Kokonendji, Célestin C. & Puig, Pedro, 2018. "Fisher dispersion index for multivariate count distributions: A review and a new proposal," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 180-193.
    6. Johann Cuenin & Bent Jørgensen & Célestin C. Kokonendji, 2016. "Simulations of full multivariate Tweedie with flexible dependence structure," Computational Statistics, Springer, vol. 31(4), pages 1477-1492, December.
    7. N. Zougab & S. Adjabi & C. Kokonendji, 2012. "Binomial kernel and Bayes local bandwidth in discrete function estimation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(3), pages 783-795.
    8. Alan Huang & Lucas Sippel & Thomas Fung, 2022. "Consistent second-order discrete kernel smoothing using dispersed Conway–Maxwell–Poisson kernels," Computational Statistics, Springer, vol. 37(2), pages 551-563, April.
    9. Peter Berkhout & Erik Plug, 2004. "A bivariate Poisson count data model using conditional probabilities," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(3), pages 349-364, August.
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    Cited by:

    1. Célestin C. Kokonendji & Sobom M. Somé & Youssef Esstafa & Marcelo Bourguignon, 2023. "On Underdispersed Count Kernels for Smoothing Probability Mass Functions," Stats, MDPI, vol. 6(4), pages 1-15, November.

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