A novel weighted likelihood estimation with empirical Bayes flavor

Summary, in English

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.

• Author: Md Mobarak Hossain; Tomasz J. Kozubowski; Krzysztof Podgórski
• Department/s: Department of Statistics
• Publishing year: 2018-02-07
• Language: English
• Pages: 392-412
• Publication/Series: Communications in Statistics: Simulation and Computation
• Volume: 47
• Issue: 2
• Links: http://dx.doi.org/10.1080/03610918.2016.1197246
• Document type: Journal article
• Publisher: Taylor & Francis
• Topic: Probability Theory and Statistics
• Keywords: Consistency; Data-dependent prior; Empirical Bayes; Exponentiated distribution; Maximum likelihood estimator; Super-efficiency; Unbounded likelihood
• Status: Published
• ISBN/ISSN/Other: ISSN: 0361-0918