Reducing the Sensitivity to Nuisance Parameters in Nonstandard Likelihood

• Activity Number: 168
• Type: Topic Contributed
• Date/Time: Monday, July 30, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Yang Ning*+
• Companies: The Johns Hopkins University
• Keywords: Composite likelihood ; Higher order inference ; Invariance ; Misspecified likelihood ; Nuisance parameters ; Pseudo likelihood

Abstract

In a parametric model, parameters are typically partitioned as parameters of interest and nuisance parameters respectively. In the likelihood based inference framework, several authors propose adjusted profile likelihoods to reduce the sensitivity to nuisance parameters. However, as the data structure becomes more complex, the inference based on the full likelihood may be inconvenient. Due to computational intractability and model misspecification, many nonstandard likelihood methods which include pseudo likelihood, composite likelihood and likelihood from a misspecified model, have been developed. Nevertheless, the modification of the nonstandard likelihood in the presence of nuisance parameters is rarely mentioned in the literature. The purpose of the current paper is to suggest a simple adjustment to the nonstandard likelihood under this circumstance. The impact of nuisance parameters is considerably reduced when adopting the proposed approach. The adjustment is still novel even if attention is restricted to the profile likelihood. Finally, the advantages of the modification are illustrated through examples and reinforced through simulations.