Understanding and Addressing the Unbounded “Likelihood” Problem.
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 maxim...
| Publicado en: | American Statistician Vol. 69; no. 3; pp. 191 - 201 |
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| Autores principales: | , , |
| Formato: | Artículo |
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Taylor & Francis Ltd
Aug2015
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| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=ssf&AN=109173235&site=ehost-live header: @attributes: shortDbName: ssf uiTerm: 109173235 longDbName: Social Sciences Full Text (H.W. Wilson) uiTag: AN controlInfo: bkinfo: jinfo: jid: 00031305 STT jtl: American Statistician issn: 00031305 maglogo: Y pubinfo: dt: Aug2015 vid: 69 iid: 3 pid: 377 pub: Taylor & Francis Ltd artinfo: ui: 109173235 10.1080/00031305.2014.1003968 ppf: 191 ppct: 10 formats: tig: atl: Understanding and Addressing the Unbounded “Likelihood” Problem. aug: au: Liu, Shiyao Wu, Huaiqing Meeker, William Q. su: Probability density function Maximum likelihood statistics Rounding errors Measurement errors Digital voltmeters sug: subj: Probability density function Maximum likelihood statistics Rounding errors Measurement errors Digital voltmeters keyword: Density approximation Interval censoring Maximum likelihood Round-off error Unbounded likelihood Density approximation Interval censoring Maximum likelihood Round-off error Unbounded likelihood ab: 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. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: N holdings: @attributes: islocal: N |
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