Adaptively robust small area estimation: Balancing robustness and efficiency of empirical bayes confidence intervals

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 γ$$ \gamma $$‐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.