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 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.

翻译：渐近无偏先验由Hartigan（1965）提出，旨在实现贝叶斯估计量的二阶无偏性。本文通过推导刻画渐近无偏先验的偏微分方程组，将Hartigan的框架推广至非独立同分布模型。此外，我们建立了此类先验存在的充要条件，并提出一种简单的构造方法。所提方法被应用于线性回归模型与嵌套误差回归模型（亦称随机效应模型）。仿真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，揭示了其在小样本场景下的有效性。