Minimum divergence estimators, maximum likelihood and exponential families
Methodology
2011-08-23 v4
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.
Cite
@article{arxiv.1108.0772,
title = {Minimum divergence estimators, maximum likelihood and exponential families},
author = {Michel Broniatowski},
journal= {arXiv preprint arXiv:1108.0772},
year = {2011}
}
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