Adaptively robust small area estimation: Balancing robustness and efficiency of empirical bayes confidence intervals
针对Fay-Herriot模型在存在异常区域时估计不可靠的问题，提出一种自适应平衡稳健性与效率的改进方法，通过优化调节参数来提升置信区间性能，适用于犯罪数量等小区域估计。
ABSTRACT Empirical Bayes (EB) small area estimation based on the well‐known Fay‐Herriot model may produce unreliable estimates when outlying areas exist. Existing robust methods against outliers or model misspecification are generally inefficient when the assumed distribution is plausible. This article proposes a simple modification of the standard EB methods with adaptively balancing robustness and efficiency. The proposed method uses ‐divergence instead of the marginal log‐likelihood and optimizes a tuning parameter controlling robustness by pursuing the efficiency of EB confidence intervals for areal parameters. We provide an asymptotic theory of the proposed method under both the correct specification of the assumed distribution and the existence of outlying areas. We investigate the numerical performance of the proposed method through simulations and two applications to small area estimation of average crime numbers.