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Title: The profile sampler
Authors: Lee, B.L. 
Kosorok, M.R.
Fine, J.P.
Keywords: Efficient Fisher information
Empirical Bayes
Frequentist inference
Markov chain Monte Carlo
Nonparametric maximum likelihood
Posterior distribution
Issue Date: Sep-2005
Citation: Lee, B.L., Kosorok, M.R., Fine, J.P. (2005-09). The profile sampler. Journal of the American Statistical Association 100 (471) : 960-969. ScholarBank@NUS Repository.
Abstract: We consider frequentist inference for the parametric component θ separately from the nuisance parameter n in semiparametric models based on sampling from the posterior of the profile likelihood. We prove that this procedure gives a first-order-correct approximation to the maximum likelihood estimator θ̂ n and consistent estimation of the efficient Fisher information for θ, without computing derivatives or using complicated numerical approximations. An exact Bayesian interpretation is established under a certain data-dependent prior. The sampler is useful in particular when the nuisance parameter is not estimable at the √n rate, where neither bootstrap validity nor general automatic variance estimation has been theoretically justified. Even when the nuisance parameter is √n consistent and the bootstrap is known to be valid, the proposed Markov chain Monte Carlo procedure can yield computational savings, because maximization of the likelihood is not required. The theory is verified for three examples. The methods are shown to perform well in simulations, and their practical utility is illustrated in two data analyses. © 2005 American Statistical Association.
Source Title: Journal of the American Statistical Association
ISSN: 01621459
DOI: 10.1198/016214504000001772
Appears in Collections:Staff Publications

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