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Title: MLE's bias pathology, model updated MLE, and Wallace's minimum message length method
Authors: Yatracos, Yannis G. 
Category: Earth and Related Environmental Sciences
Field: Engineering and Technology
Issue Date: 1-Mar-2015
Publisher: Institute of Electrical and Electronics Engineers Inc.
Source: IEEE Transactions on Information Theory Volume 61, Issue 3, 1 March 2015, Article number 6998937, Pages 1426-1431
DOI: 10.1109/TIT.2014.2386329
Abstract: The inherent bias pathology of the maximum likelihood estimation method is confirmed for models with unknown parameters θ and ψ when maximum likelihood estimate (MLE) ψ is function of MLE θ. To reduce ψ's bias the likelihood equation to be solved for ψ is updated using the model for the data Y in it. For various models with ψ a shape parameter model updated (MU) MLE, ψMU, reduces ψ's bias. For the Pareto model ψMU reduces in addition ψ's variance. The results explain the difference that puzzled Fisher, between biased ψ and the unbiased estimate he obtained for two models with the abandoned two-stage procedure used in MUMLE's implementation. ψMU is also obtained with the minimum message length method thus motivating the use of priors in frequentist inference.
ISSN: 00189448
Rights: © 2014 IEEE.
Type: Article
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