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A smoothed semiparametric likelihood for estimation of nonparametric finite mixture models with a copula-based dependence structure

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  • Michael Levine

    (Purdue University)

  • Gildas Mazo

    (INRAE, MaIAGE)

Abstract

In this manuscript, we consider a finite multivariate nonparametric mixture model where the dependence between the marginal densities is modeled using the copula device. Pseudo expectation–maximization (EM) stochastic algorithms were recently proposed to estimate all of the components of this model under a location-scale constraint on the marginals. Here, we introduce a deterministic algorithm that seeks to maximize a smoothed semiparametric likelihood. No location-scale assumption is made about the marginals. The algorithm is monotonic in one special case, and, in another, leads to “approximate monotonicity”—whereby the difference between successive values of the objective function becomes non-negative up to an additive term that becomes negligible after a sufficiently large number of iterations. The behavior of this algorithm is illustrated on several simulated and real datasets. The results suggest that, under suitable conditions, the proposed algorithm may indeed be monotonic in general. A discussion of the results and some possible future research directions round out our presentation.

Suggested Citation

  • Michael Levine & Gildas Mazo, 2024. "A smoothed semiparametric likelihood for estimation of nonparametric finite mixture models with a copula-based dependence structure," Computational Statistics, Springer, vol. 39(4), pages 1825-1846, June.
    • Handle: RePEc:spr:compst:v:39:y:2024:i:4:d:10.1007_s00180-024-01483-4
    DOI: 10.1007/s00180-024-01483-4
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    References listed on IDEAS

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    1. Hiroyuki Kasahara & Katsumi Shimotsu, 2014. "Non-parametric identification and estimation of the number of components in multivariate mixtures," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 97-111, January.
    2. Stéphane Bonhomme & Koen Jochmans & Jean-Marc Robin, 2016. "Non-parametric estimation of finite mixtures from repeated measurements," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 211-229, January.
    3. Mazo, Gildas, 2017. "A Semiparametric and Location-Shift Copula-Based Mixture Model," LIDAM Reprints ISBA 2017043, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. M. Levine & D. R. Hunter & D. Chauveau, 2011. "Maximum smoothed likelihood for multivariate mixtures," Biometrika, Biometrika Trust, vol. 98(2), pages 403-416.
    5. Mazo, Gildas & Averyanov, Yaroslav, 2019. "Constraining kernel estimators in semiparametric copula mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 170-189.
    6. Gildas Mazo, 2017. "A Semiparametric and Location-Shift Copula-Based Mixture Model," Journal of Classification, Springer;The Classification Society, vol. 34(3), pages 444-464, October.
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