A SECOND-ORDER EFFICIENT EMPIRICAL BAYES CONFIDENCE INTERVAL

• 成果类型: Article
• 署名作者: Yoshimori, Masayo; Lahiri, Partha
• 署名单位: University of Osaka; University System of Maryland; University of Maryland College Park
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/14-AOS1219
• 发表日期: 2014
• 页码: 1233-1261
• 关键词: mean squared error; small-area estimators; prediction intervals; MODEL; maximum

摘要

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 O(m(-3/2)). 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 0(m-3/2). The proposed method is not simulation-based and requires only a fraction of computing time needed for the corresponding parametric bootstrap empirical Bayes confidence interval. A Monte Carlo simulation study demonstrates the superiority of the proposed method over other competing methods.