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Article Dans Une Revue Statistics and Probability Letters Année : 2014

Minimum divergence estimators, maximum likelihood and exponential families

Résumé

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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Dates et versions

hal-00613126 , version 1 (02-08-2011)
hal-00613126 , version 2 (03-08-2011)
hal-00613126 , version 3 (06-08-2011)
hal-00613126 , version 4 (07-08-2011)
hal-00613126 , version 5 (19-08-2011)

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