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August 2008 Higher order semiparametric frequentist inference with the profile sampler
Guang Cheng, Michael R. Kosorok
Ann. Statist. 36(4): 1786-1818 (August 2008). DOI: 10.1214/07-AOS523

Abstract

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 in [J. American Statist. Assoc. 100 (2005) 960–969] 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 α can be estimated by the α-level credible set from the profile sampler with an error of order OP(n−1). Simulation studies are used to assess second-order asymptotic validity of the profile sampler. As far as we are aware, these are the first higher order accuracy results for semiparametric frequentist inference.

Citation

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Guang Cheng. Michael R. Kosorok. "Higher order semiparametric frequentist inference with the profile sampler." Ann. Statist. 36 (4) 1786 - 1818, August 2008. https://doi.org/10.1214/07-AOS523

Information

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

zbMATH: 1142.62030
MathSciNet: MR2435456
Digital Object Identifier: 10.1214/07-AOS523

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

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.36 • No. 4 • August 2008
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