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August 2008 General frequentist properties of the posterior profile distribution
Guang Cheng, Michael R. Kosorok
Ann. Statist. 36(4): 1819-1853 (August 2008). DOI: 10.1214/07-AOS536

Abstract

In this paper, inference for the parametric component of a semiparametric model based on sampling from the posterior profile distribution is thoroughly investigated from the frequentist viewpoint. The higher-order validity of the profile sampler obtained in Cheng and Kosorok [Ann. Statist. 36 (2008)] is extended to semiparametric models in which the infinite dimensional nuisance parameter may not have a root-n convergence rate. This is a nontrivial extension because it requires a delicate analysis of the entropy of the semiparametric models involved. We find that the accuracy of inferences based on the profile sampler improves as the convergence rate of the nuisance parameter increases. Simulation studies are used to verify this theoretical result. We also establish that an exact frequentist confidence interval obtained by inverting the profile log-likelihood ratio can be estimated with higher-order accuracy by the credible set of the same type obtained from the posterior profile distribution. Our theory is verified for several specific examples.

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Guang Cheng. Michael R. Kosorok. "General frequentist properties of the posterior profile distribution." Ann. Statist. 36 (4) 1819 - 1853, August 2008. https://doi.org/10.1214/07-AOS536

Information

Published: August 2008
First available in Project Euclid: 16 July 2008

zbMATH: 1142.62031
MathSciNet: MR2435457
Digital Object Identifier: 10.1214/07-AOS536

Subjects:
Primary: 62F25 , 62G20
Secondary: 62F12 , 62F15

Keywords: Cox proportional hazards model , higher-order frequentist inference , Markov chain Monte Carlo , partly linear regression model , profile likelihood , semiparametric models

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.36 • No. 4 • August 2008
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