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This is a Quantitative Study study.

October 8, 2025

Priors for second-order unbiased Bayes estimators

Key Points

Deriving conditions for asymptotically unbiased priors improves the accuracy of Bayes estimators in various settings.
A system of partial differential equations characterizes the necessary conditions for these priors to exist.
Application to the linear regression model demonstrates the practical utility of the derived priors in real-world scenarios.
Simulation studies affirm the effectiveness of the proposed estimator in small-sample scenarios, supporting its real-world applicability.

Abstract

Summary Asymptotically unbiased priors, introduced by Hartigan (1965), are designed to achieve second-order unbiasedness of Bayes estimators. This paper extends Hartigan’s framework to non-independent-and-identically-distributed models by deriving a system of partial differential equations that characterizes asymptotically unbiased priors. Furthermore, we establish a necessary and sufficient condition for the existence of such priors and propose a simple procedure for constructing them. The proposed method is applied to the linear regression model and the nested error regression model (also known as the random effects model). Simulation studies evaluate the frequentist properties of the Bayes estimator under the asymptotically unbiased prior for the nested error regression model, highlighting its effectiveness in small-sample settings.

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