A highly accurate simple small area confidence interval method

We introduce a new adjusted residual maximum likelihood method in the context of producing an empirical Bayes confidence interval for a normal mean, a problem of great interest in different small area applications. Like other rival empirical Bayes confidence intervals such as the well-known parametric boot-strap method, the proposed interval is second-order correct. The proposed in-terval is carefully constructed so that it always produces an interval shorter than the corresponding maximum likelihood based direct confidence interval, a property not analytically proved for other competing methods. Moreover, the proposed method is not simulation-based and requires only a fraction of com-puting time needed for the parametric bootstrap confidence interval. A Monte Carlo simulation study demonstrates the superiority of the proposed method over other competing methods