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-i.i.d. 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 several examples, including the linear regression model and the nested error regression (NER) 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 NER model, highlighting its effectiveness in small-sample settings.

翻译：Hartigan (1965) 引入的渐近无偏先验旨在实现贝叶斯估计量的二阶无偏性。本文通过推导一个刻画渐近无偏先验的偏微分方程组，将 Hartigan 的框架推广到非独立同分布模型。此外，我们建立了此类先验存在的一个充要条件，并提出了一种构造它们的简单方法。所提出的方法被应用于多个示例，包括线性回归模型和嵌套误差回归模型（亦称为随机效应模型）。模拟研究评估了嵌套误差回归模型在渐近无偏先验下贝叶斯估计量的频率性质，突显了其在小样本设置中的有效性。