Higher order semiparametric frequentist inference with the profile sampler

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 $\alpha$ can be estimated by the $\alpha$-level credible set from the profile sampler with an error of order $O_P(n^{-1})$. 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.

Published in at http://dx.doi.org/10.1214/07-AOS523 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• Two likelihood-based semiparametric estimation methods for panel count data with covariates
• Robust Inference for Univariate Proportional Hazards Frailty Regression Models
• Penalized maximum likelihood and semiparametric second-order efficiency

Cited by in corpus (5)

• Bootstrap consistency for general semiparametric $M$-estimation
• General frequentist properties of the posterior profile distribution
• Bayesian frequentist hybrid inference
• Semiparametric Bernstein-von Mises Theorem: Second Order Studies
• Convergence Rate of K-Step Maximum Likelihood Estimate in Semiparametric Models