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A novel weighted likelihood estimation with empirical Bayes flavor

Hossain, Md Mobarak; Kozubowski, Tomasz J. and Podgórski, Krzysztof LU (2017) In Communications in Statistics: Simulation and Computation
Abstract

We propose a novel approach to estimation, where a set of estimators of a parameter is combined into a weighted average to produce the final estimator. The weights are chosen to be proportional to the likelihood evaluated at the estimators. We investigate the method for a set of estimators obtained by using the maximum likelihood principle applied to each individual observation. The method can be viewed as a Bayesian approach with a data-driven prior distribution. We provide several examples illustrating the new method and argue for its consistency, asymptotic normality, and efficiency. We also conduct simulation studies to assess the performance of the estimators. This straightforward methodology produces consistent estimators... (More)

We propose a novel approach to estimation, where a set of estimators of a parameter is combined into a weighted average to produce the final estimator. The weights are chosen to be proportional to the likelihood evaluated at the estimators. We investigate the method for a set of estimators obtained by using the maximum likelihood principle applied to each individual observation. The method can be viewed as a Bayesian approach with a data-driven prior distribution. We provide several examples illustrating the new method and argue for its consistency, asymptotic normality, and efficiency. We also conduct simulation studies to assess the performance of the estimators. This straightforward methodology produces consistent estimators comparable with those obtained by the maximum likelihood method. The method also approximates the distribution of the estimator through the “posterior” distribution.

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author
organization
publishing date
type
Contribution to journal
publication status
epub
subject
keywords
Consistency, Data-dependent prior, Empirical Bayes, Exponentiated distribution, Maximum likelihood estimator, Super-efficiency, Unbounded likelihood
in
Communications in Statistics: Simulation and Computation
pages
21 pages
publisher
Taylor & Francis
external identifiers
  • scopus:85038407848
ISSN
0361-0918
DOI
10.1080/03610918.2016.1197246
language
English
LU publication?
yes
id
9a153356-a515-456b-b7cc-9e4ce47a863a
date added to LUP
2018-01-03 10:52:33
date last changed
2018-01-08 14:04:12
@article{9a153356-a515-456b-b7cc-9e4ce47a863a,
  abstract     = {<p>We propose a novel approach to estimation, where a set of estimators of a parameter is combined into a weighted average to produce the final estimator. The weights are chosen to be proportional to the likelihood evaluated at the estimators. We investigate the method for a set of estimators obtained by using the maximum likelihood principle applied to each individual observation. The method can be viewed as a Bayesian approach with a data-driven prior distribution. We provide several examples illustrating the new method and argue for its consistency, asymptotic normality, and efficiency. We also conduct simulation studies to assess the performance of the estimators. This straightforward methodology produces consistent estimators comparable with those obtained by the maximum likelihood method. The method also approximates the distribution of the estimator through the “posterior” distribution.</p>},
  author       = {Hossain, Md Mobarak and Kozubowski, Tomasz J. and Podgórski, Krzysztof},
  issn         = {0361-0918},
  keyword      = {Consistency,Data-dependent prior,Empirical Bayes,Exponentiated distribution,Maximum likelihood estimator,Super-efficiency,Unbounded likelihood},
  language     = {eng},
  month        = {12},
  pages        = {21},
  publisher    = {Taylor & Francis},
  series       = {Communications in Statistics: Simulation and Computation},
  title        = {A novel weighted likelihood estimation with empirical Bayes flavor},
  url          = {http://dx.doi.org/10.1080/03610918.2016.1197246},
  year         = {2017},
}