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

TL;DR

This paper introduces an adaptive empirical Bayes method for small area estimation that balances robustness against outliers with efficiency, using gamma-divergence and tuning parameter optimization.

Contribution

It proposes a novel adaptive modification of empirical Bayes methods employing gamma-divergence to improve robustness and efficiency in small area estimation.

Findings

The method effectively balances robustness and efficiency.

Asymptotic theory supports the method's reliability.

Simulation and real data demonstrate improved performance.

Abstract

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.