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Minimum Divergence Estimators, Maximum Likelihood and the Generalized Bootstrap.

Michel Broniatowski1

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

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Summary
This summary is machine-generated.

Minimum divergence estimators are maximum likelihood estimators (MLEs) for generalized bootstrapped sampling. This study examines the optimality of associated tests of fit under these schemes.

Keywords:
Bahadur efficiencybootstrapconditional limit theoremmaximum likelihoodminimum divergence estimatorstatistical divergences

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Area of Science:

  • Statistics
  • Statistical Inference

Background:

  • Minimum divergence estimators are widely used in statistical modeling.
  • Maximum likelihood estimators (MLEs) are a common class of estimators.
  • Generalized bootstrapped sampling schemes offer advantages in certain statistical applications.

Purpose of the Study:

  • To investigate the relationship between minimum divergence estimators and MLEs.
  • To analyze the performance of these estimators under generalized bootstrapped sampling.
  • To consider the optimality of tests of fit within this framework.

Main Methods:

  • The study focuses on minimum divergence estimators.
  • It considers maximum likelihood estimators (MLEs) in the context of generalized bootstrapped sampling.
  • Bahadur's definition of optimality for tests of fit is applied.

Main Results:

  • Most commonly used minimum divergence estimators are identified as MLEs for specific generalized bootstrapped sampling schemes.
  • The optimality of associated tests of fit under these sampling schemes is considered.

Conclusions:

  • The findings link minimum divergence estimation with MLEs under generalized bootstrapped sampling.
  • The study provides insights into the theoretical properties of statistical tests in these settings.