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- W4300668841 abstract "The inherent bias pathology of the maximum likelihood (ML) estimation method is confirmed for models with unknown parameters $theta$ and $psi$ when MLE $hat psi$ is function of MLE $hat theta.$ To reduce $hat psi$'s bias the likelihood equation to be solved for $psi$ is updated using the model for the data $Y$ in it. Model updated (MU) MLE, $hat psi_{MU},$ often reduces either totally or partially $hat psi$'s bias when estimating shape parameter $psi.$ For the Pareto model $hat psi_{MU}$ reduces also $hat psi$'s variance. The results explain the difference that puzzled R. A. Fisher, between biased $hat psi$ and the unbiased estimate he obtained for two models with the 2-stage procedure. MUMLE's implementation is equivalent to the abandoned 2-stage procedure thus justifying its use. MUMLE and Firth's bias correcting likelihood are also obtained with the Minimum Message Length method thus motivating its use in frequentist inference and, more generally, model updating with a prior distribution." @default.
- W4300668841 created "2022-10-04" @default.
- W4300668841 creator A5029862399 @default.
- W4300668841 date "2013-12-30" @default.
- W4300668841 modified "2023-09-26" @default.
- W4300668841 title "MLE's bias pathology, Model Updated Maximum Likelihood Estimates and Wallace's Minimum Message Length method" @default.
- W4300668841 doi "https://doi.org/10.48550/arxiv.1312.7713" @default.
- W4300668841 hasPublicationYear "2013" @default.
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