Bootstrap validity in Bayesian semi-parametric models
Magid Sabbagh, David A. Stephens
math.ST, stat.ML, stat.TH
Submitted: 2026-08-07
Updated: 2026-08-10
Comments: 17 pages
License: http://creativecommons.org/licenses/by-nc-nd/4.0/
The gist: We discuss Bayesian inference on a low-dimensional targeted parameter in the presence of possibly highly complex nuisance components within the semi-parametric inference framework using an estimating
Terminology
Abstract
We discuss Bayesian inference on a low-dimensional targeted parameter in the presence of possibly highly complex nuisance components within the semi-parametric inference framework using an estimating function approach. We obtain a posterior distribution using non-parametric Bayesian methods through the Dirichlet process and the Bayesian bootstrap. We relax the commonly deployed notion of stochastic equicontinuity and develop a framework leading to posterior inference with good frequentist properties, specifically we demonstrate that the posterior distribution is asymptotically Normal and concentrates at the true value of the parameter. We emphasize the specific assumptions that are required to obtain these results, and how relaxing any of them alters the conclusions. We verify the analytical results in simulation.
Sources
- Posterior Uncertainty for Targeted Parameters in Bayesian Bootstrap Procedures
- Semi-parametric Bayesian inference under Neyman orthogonality
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