Masayo Yoshimori, Partha Lahiri
Abstract
We introduce a new adjusted residual maximum likelihood method (REML) in the context of producing an empirical Bayes (EB) 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 bootstrap empirical Bayes method, the proposed interval is second-order correct, that is, the proposed interval has a coverage error of order . Moreover, the proposed interval is carefully constructed so that it always produces an interval shorter than the corresponding direct confidence interval, a property not analytically proved for other competing methods that have the same coverage error of order