Adjusted Profile Likelihood for Two-Parameter Exponential Family Models

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 family
• Information bias
• Likelihood
• Likelihood ratio test
• Nuisance parameter
• Profile likelihood
• Score bias