  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.
