### A novel weighted likelihood estimation with empirical Bayes flavor

(2015) In Working Papers in Statistics- Abstract
- We propose a novel approach to estimation, where each individual observation in a random sample is used to derive an estimator of an unknown parameter using the maximum likelihood principle. These individual estimators are then combined as a weighted average to produce the final estimator. The weights are chosen to be proportional to the likelihood function evaluated at the estimators based on each observation. The method can be related to a Bayesian approach, where the prior distribution is data driven. In case of estimating a location parameter of a unimodal density, the prior distribution is the empirical distribution of the sample, and converges to the true distribution that generated the data as the sample size increases.

... (More) - We propose a novel approach to estimation, where each individual observation in a random sample is used to derive an estimator of an unknown parameter using the maximum likelihood principle. These individual estimators are then combined as a weighted average to produce the final estimator. The weights are chosen to be proportional to the likelihood function evaluated at the estimators based on each observation. The method can be related to a Bayesian approach, where the prior distribution is data driven. In case of estimating a location parameter of a unimodal density, the prior distribution is the empirical distribution of the sample, and converges to the true distribution that generated the data as the sample size increases.

We provide several examples illustrating the new method, argue for its consistency, and conduct simulation studies to assess the performance of the estimators. It turns out that this straightforward methodology produces consistent estimators, which seem to be comparable with those obtained by the maximum likelihood method. (Less)

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Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/8052689

- author
- Hossain, Mobarak
; Kozubowski, Tomasz
and Podgorski, Krzysztof
^{LU} - organization
- publishing date
- 2015
- type
- Working paper/Preprint
- publication status
- published
- subject
- keywords
- Consistency, data-dependent prior, empirical Bayes, exponentiated distribution, location parameter, maximum likelihood estimator, super-efficiency, unbounded likelihood
- in
- Working Papers in Statistics
- issue
- 6
- pages
- 28 pages
- publisher
- Department of Statistics, Lund university
- language
- English
- LU publication?
- yes
- id
- ccf31357-b6ca-4608-9fd6-6104d952c20e (old id 8052689)
- alternative location
- http://journals.lub.lu.se/index.php/stat/article/view/15037
- date added to LUP
- 2016-04-04 09:58:09
- date last changed
- 2018-11-21 20:55:56

@misc{ccf31357-b6ca-4608-9fd6-6104d952c20e, abstract = {{We propose a novel approach to estimation, where each individual observation in a random sample is used to derive an estimator of an unknown parameter using the maximum likelihood principle. These individual estimators are then combined as a weighted average to produce the final estimator. The weights are chosen to be proportional to the likelihood function evaluated at the estimators based on each observation. The method can be related to a Bayesian approach, where the prior distribution is data driven. In case of estimating a location parameter of a unimodal density, the prior distribution is the empirical distribution of the sample, and converges to the true distribution that generated the data as the sample size increases.<br/><br> <br/><br> We provide several examples illustrating the new method, argue for its consistency, and conduct simulation studies to assess the performance of the estimators. It turns out that this straightforward methodology produces consistent estimators, which seem to be comparable with those obtained by the maximum likelihood method.}}, author = {{Hossain, Mobarak and Kozubowski, Tomasz and Podgorski, Krzysztof}}, keywords = {{Consistency; data-dependent prior; empirical Bayes; exponentiated distribution; location parameter; maximum likelihood estimator; super-efficiency; unbounded likelihood}}, language = {{eng}}, note = {{Working Paper}}, number = {{6}}, publisher = {{Department of Statistics, Lund university}}, series = {{Working Papers in Statistics}}, title = {{A novel weighted likelihood estimation with empirical Bayes flavor}}, url = {{https://lup.lub.lu.se/search/files/5429067/8054204.pdf}}, year = {{2015}}, }