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Minimum divergence estimators, maximum likelihood and exponential families

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  • Broniatowski, Michel

Abstract

The dual representation formula of the divergence between two distributions in a parametric model is presented. Resulting estimators do not make use of any grouping or smoothing. For smooth divergences they all coincide with the MLE on any regular exponential family.

Suggested Citation

  • Broniatowski, Michel, 2014. "Minimum divergence estimators, maximum likelihood and exponential families," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 27-33.
    • Handle: RePEc:eee:stapro:v:93:y:2014:i:c:p:27-33
    DOI: 10.1016/j.spl.2014.06.014
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    References listed on IDEAS

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    1. Broniatowski, M. & Leorato, S., 2006. "An estimation method for the Neyman chi-square divergence with application to test of hypotheses," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1409-1436, July.
    2. Toma, Aida & Broniatowski, Michel, 2011. "Dual divergence estimators and tests: Robustness results," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 20-36, January.
    3. Broniatowski, Michel & Keziou, Amor, 2009. "Parametric estimation and tests through divergences and the duality technique," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 16-36, January.
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    Cited by:

    1. Diaa Al Mohamad, 2018. "Towards a better understanding of the dual representation of phi divergences," Statistical Papers, Springer, vol. 59(3), pages 1205-1253, September.
    2. Jitka Hrabáková & Václav Kůs, 2017. "Notes on consistency of some minimum distance estimators with simulation results," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(2), pages 243-257, February.
    3. Gayen, Atin & Kumar, M. Ashok, 2021. "Projection theorems and estimating equations for power-law models," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    4. Ayman Hijazy & András Zempléni, 2021. "Gamma Process-Based Models for Disease Progression," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 241-255, March.

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