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Activity Number:
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292
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Type:
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Contributed
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Date/Time:
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Tuesday, August 8, 2006 : 10:30 AM to 12:20 PM
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Sponsor:
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Section on Bayesian Statistical Science
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| Abstract - #306066 |
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Title:
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Higher Order Semiparametric Frequentist Inference Based on the Profile Sampler
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Author(s):
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Guang Cheng*+ and Michael Kosorok
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Companies:
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University of Wisconsin-Madison and University of Wisconsin-Madison
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Address:
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Department of Statistics, Madison, WI, 53706,
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Keywords:
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higher order frequentist inference ; Markov chain Monte Carlo ; profile likelihood ; the Cox proportional hazards model ; the proportional odds model ; case-studies with a missing covariate
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Abstract:
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We consider higher order frequentist inference for the parametric component of a semiparametric model based on sampling from the posterior profile distribution. The first order validity of this procedure established by Lee, Kosorok and Fine (2005) is extended to second order validity in the setting where the infinite dimensional nuisance parameter achieves the parametric rate. Specifically, we obtain higher order estimates of the maximum profile likelihood estimator and of the efficient Fisher information. Moreover, we prove that an exact frequentist confidence interval for the parametric component at level alpha can be estimated by the alpha level credible set from the profile sampler with error of order $O_P(n^{-1})$. As far as we are aware, these results are the first higher order frequentist results obtained for semiparametric estimation. The theory is verified for three examples.
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