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De Bin, Riccardo; Sartori, Nicola; Severini, Thomas A. (26. February 2014): Integrated likelihoods in models with stratum nuisance parameters. Department of Statistics: Technical Reports, No.157




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 the integrated likelihood, if chosen wisely, largely outperforms standard likelihood methods, such as the profile likelihood. These results are confirmed by simulation studies, in which comparisons with modified profile likelihood are also considered.