Minimum Divergence Estimators, Maximum Likelihood and the Generalized Bootstrap

Michel Broniatowski

doi:10.3390/e23020185

Minimum Divergence Estimators, Maximum Likelihood and the Generalized Bootstrap

Entropy (Basel). 2021 Jan 31;23(2):185. doi: 10.3390/e23020185.

Author

Michel Broniatowski¹

Affiliation

¹ Faculté de Mathématiques, Laboratoire de Probabilité, Statistique et Modélisation, Université Pierre et Marie Curie (Sorbonne Université), 4 Place Jussieu, CEDEX 05, 75252 Paris, France.

Abstract

This paper states that most commonly used minimum divergence estimators are MLEs for suited generalized bootstrapped sampling schemes. Optimality in the sense of Bahadur for associated tests of fit under such sampling is considered.

Keywords: Bahadur efficiency; bootstrap; conditional limit theorem; maximum likelihood; minimum divergence estimator; statistical divergences.