2005•Communication in Statistics- Theory and MethodsRequires access

Adjusted Profile Likelihood for Two-Parameter Exponential Family Models

Silvia L. P. Ferrari, Michel Ferreira da Silva, Francisco Cribari‐Neto

Abstract

Abstract Abstract This article presents several different adjustments for profile likelihoods in the two-parameter exponential family. These adjustments aim at reducing the impact of the nuisance parameter on the likelihood-based inference regarding the parameter of interest. Several particular cases are considered. The expressions we provide for the different adjustments are simple and can be computed easily. Numerical results comparing the different approaches in small samples are also presented. Overall, the adjustments considered proved to lead to more reliable inference than the usual (profile) likelihood approach. Additionally, no adjusment uniformly outperformed the others. Key Words: Exponential familyInformation biasLikelihoodLikelihood ratio testNuisance parameterProfile likelihoodScore bias

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Key concepts: Exponential family, Nuisance parameter, Inference, Maximum likelihood, Simple (philosophy), Exponential function, Mathematics, Statistics