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Ventura, Laura and Racugno, Walter (2011) On interval and point estimators based on a penalization of the modified profile likelihood. [Working Paper] WORKING PAPER SERIES . , PADOVA ISBN 2/2011

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Abstract (english)

Various modifications of the profile likelihood have been proposed in the literature. Despite modified profile likelihood methods have better properties than those based on the profile likelihood, the signed likelihood ratio statistic based on the modified profile likelihood has a standard normal distribution only to first order, and it can be inaccurate in particular in models with many nuisance parameters. In this paper we propose an adjustment of the profile likelihood from a new perspective. The idea is to resort to suitable default priors on the parameter of interest only to be used as non-negative weight functions in order to modify the modified profile likelihood. In particular, we focus on matching priors, i.e. priors on the parameter of interest only for which there is an agreement between frequentist and Bayesian inference, derived from modified profile likelihoods. The proposed modified profile likelihood has desiderable inferential properties: the corresponding signed likelihood ratio statistic is standard normal to second order and the correponding maximizer is a refinement of the maximum likelihood estimator, which improves its small sample properties. Examples illustrate the proposed modified profile likelihood and outline its improvement over its counterparts.


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EPrint type:Working Paper
Anno di Pubblicazione:February 2011
More information:Pubblicato anche in: Statistics and Probability Letters, (2012) 82, 1285-1289
Key Words:Bayesian inference, Exponential family, Group model, Higher-order asymptotics, Modified profile likelihood, Nuisance parameter, Skew-normal distribution, Signed and modified signed likelihood ratio statistic.
Settori scientifico-disciplinari MIUR:Area 13 - Scienze economiche e statistiche > SECS-S/01 Statistica
Struttura di riferimento:Dipartimenti > Dipartimento di Scienze Statistiche
Codice ID:8786
Depositato il:12 May 2015 16:41
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