Priors for second-order unbiased Bayes estimators
本文扩展了Hartigan的渐近无偏先验框架到非独立同分布模型，通过偏微分方程组刻画先验，给出存在性条件与构造方法，并在线性回归和嵌套误差回归模型中验证了其在小样本下的有效性。
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.