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Empirical Bayes small area estimation based on the well-known Fay-Herriotmodel may produce unreliable estimates when outlying areas exist. Existingrobust methods against outliers or model misspecification are generallyinefficient when the assumed distribution is plausible. This paper proposes asimple modification of the standard empirical Bayes methods with adaptivelybalancing robustness and efficiency. The proposed method employsgamma-divergence instead of the marginal log-likelihood and optimizes a tuningparameter controlling robustness by pursuing the efficiency of empirical Bayesconfidence intervals for areal parameters. We provide an asymptotic theory ofthe proposed method under both the correct specification of the assumeddistribution and the existence of outlying areas. We investigate the numericalperformance of the proposed method through simulations and an application tosmall area estimation of average crime numbers.

Adaptively Robust Small Area Estimation: Balancing Robustness and Efficiency of Empirical Bayes Confidence Intervals