Understanding and Addressing the Unbounded “Likelihood” Problem

dc.contributor.author Liu, Shiyao
dc.contributor.author Wu, Huaiqing
dc.contributor.author Meeker, William
dc.contributor.department Statistics
dc.date 2019-12-20T17:52:58.000
dc.date.accessioned 2020-07-02T06:57:35Z
dc.date.available 2020-07-02T06:57:35Z
dc.date.copyright Thu Jan 01 00:00:00 UTC 2015
dc.date.issued 2015-08-01
dc.description.abstract <p>The joint probability density function, evaluated at the observed data, is commonly used as the likelihood function to compute maximum likelihood estimates. For some models, however, there exist paths in the parameter space along which this density-approximation likelihood goes to infinity and maximum likelihood estimation breaks down. In all applications, however, observed data are really discrete due to the round-off or grouping error of measurements. The “correct likelihood” based on interval censoring can eliminate the problem of an unbounded likelihood. This article categorizes the models leading to unbounded likelihoods into three groups and illustrates the density-approximation breakdown with specific examples. Although it is usually possible to infer how given data were rounded, when this is not possible, one must choose the width for interval censoring, so we study the effect of the round-off on estimation. We also give sufficient conditions for the joint density to provide the same maximum likelihood estimate as the correct likelihood, as the round-off error goes to zero.</p>
dc.description.comments <p>This is an Accepted Manuscript of an article published by Taylor & Francis as Liu, Shiyao, Huaiqing Wu, and William Q. Meeker. "Understanding and addressing the unbounded “likelihood” problem." <em>The American Statistician</em> 69, no. 3 (2015): 191-200. DOI: <a href="http://dx.doi.org/10.1080/00031305.2014.1003968" target="_blank">10.1080/00031305.2014.1003968</a>. Posted with permission.</p>
dc.format.mimetype application/pdf
dc.identifier archive/lib.dr.iastate.edu/stat_las_pubs/274/
dc.identifier.articleid 1281
dc.identifier.contextkey 15237871
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath stat_las_pubs/274
dc.identifier.uri https://dr.lib.iastate.edu/handle/20.500.12876/90592
dc.language.iso en
dc.source.uri https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1088&context=stat_las_preprints
dc.subject.disciplines Statistics and Probability
dc.subject.keywords Density approximation
dc.subject.keywords Interval censoring
dc.subject.keywords Maximum likelihood
dc.subject.keywords Round-off error
dc.subject.keywords Unbounded likelihood
dc.title Understanding and Addressing the Unbounded “Likelihood” Problem
dc.type article
dc.type.genre article
dspace.entity.type Publication
relation.isOrgUnitOfPublication 264904d9-9e66-4169-8e11-034e537ddbca