Empirical Bayes 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 paper proposes a simple modification of the standard empirical Bayes methods with adaptively balancing robustness and efficiency. The proposed method employs gamma-divergence instead of the marginal log-likelihood and optimizes a tuning parameter controlling robustness by pursuing the efficiency of empirical Bayes 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 an application to small area estimation of average crime numbers.

翻译：根据众所周知的Fay-Herriot 模型对贝雅山进行的经验性小面积估计,在存在外围地带时,可能产生不可靠的估计。现有的防止外围地带或模型偏差的可靠方法在假定分布合理时一般是效率低下的。本文件建议简单修改标准的经验性贝雅山脉方法,在适应性上平衡稳健性和效率。拟议方法采用伽马比亚法,而不是边际对原木的相似性,并通过追求经验性贝雅斯信任区间对等参数的效率,优化调控参数,以控制稳健性。我们根据假设分布的正确规格和外围地带的存在,对拟议方法提供了一种不严谨的理论。我们通过模拟和对平均犯罪数字进行小面积估计,对拟议方法的数字性进行了调查。