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Minimum divergence estimators, maximum likelihood and exponential families

Abstract : In this note we prove the dual representation formula of the divergence between two distributions in a parametric model. Resulting estimators for the divergence as for the parameter are derived. These estimators do not make use of any grouping nor smoothing. It is proved that all differentiable divergences induce the same estimator of the parameter on any regular exponential family, which is nothing else but the MLE.
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Contributor : Michel Broniatowski <>
Submitted on : Friday, August 19, 2011 - 4:49:13 PM
Last modification on : Monday, May 4, 2020 - 3:50:13 PM
Long-term archiving on: : Friday, November 25, 2011 - 11:36:54 AM


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  • HAL Id : hal-00613126, version 5
  • ARXIV : 1108.0772


Michel Broniatowski. Minimum divergence estimators, maximum likelihood and exponential families. Statistics and Probability Letters, Elsevier, 2014, 93 (6), pp.27-33. ⟨hal-00613126v5⟩



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