The Annals of Statistics

Higher order semiparametric frequentist inference with the profile sampler

Guang Cheng and Michael R. Kosorok

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 36, Number 4 (2008), 1786-1818.

Dates
First available in Project Euclid: 16 July 2008

Permanent link to this document
https://projecteuclid.org/euclid.aos/1216237300

Digital Object Identifier
doi:10.1214/07-AOS523

Mathematical Reviews number (MathSciNet)
MR2435456

Zentralblatt MATH identifier
1142.62030

Subjects
Primary: 62G20: Asymptotic properties 62F25: Tolerance and confidence regions
Secondary: 62F15: Bayesian inference 62F12: Asymptotic properties of estimators

Keywords
Higher order frequentist inference posterior distribution Markov chain Monte Carlo profile likelihood Cox proportional hazards model proportional odds model case-control studies with a missing covariate

Citation

Cheng, Guang; Kosorok, Michael R. Higher order semiparametric frequentist inference with the profile sampler. Ann. Statist. 36 (2008), no. 4, 1786--1818. doi:10.1214/07-AOS523. https://projecteuclid.org/euclid.aos/1216237300


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