Integrated likelihoods in models with stratum nuisance parameters

Abstract

Frequentist inference about a parameter of interest in presence of a nuisance parameter can be based on an integrated likelihood function. We analyze the behaviour of inferential quantities based on such a pseudo-likelihood in a two-index-asymptotics framework, in which both sample size and dimension of the nuisance parameter may diverge to infinity. We show that a properly chosen integrated likelihood largely outperforms standard likelihood methods, such as those based on the profile likelihood. These results are confirmed by simulation studies, in which comparisons with modified profile likelihood are also considered.