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Minimum divergence estimators,maximum likelihood and exponential families
Institution:1. MAP5, UMR 8145 CNRS, Sorbonne Paris Cité, Paris Descartes University, France;2. Sorbonne Universités, Université Pierre et Marie Curie, UMR 7599 CNRS, Laboratoire de Probabilités et Modèles aléatoires, France;1. Department of Physics, Zhejiang University, Hangzhou 310027, PR China;2. Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, B?ehová 7, 115 19 Praha 1, Czech Republic;3. U?ak University, Faculty of Art and Sciences, Department of Statistics, U?ak, Turkey;1. Department of Statistics, Central China Normal University, Wuhan 430079, China;2. Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt;1. Department of Mathematics & Statistics, University of Ottawa, 585 King Edward, Ottawa ON K1N 6N5, Canada;2. School of Mathematics & Statistics, University of Sydney, NSW 2006, Australia;1. Department of Mathematics, University of Beira Interior, Covilhã, Portugal;2. Center of Mathematics of Minho University, Braga, Portugal
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.
Keywords:Statistical divergence  Minimum divergence estimator  Maximum likelihood  Exponential family
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