A second-order efficient empirical bayes confidence interval

Masayo Yoshimori, Partha Lahiri

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)


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 O(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.

Original languageEnglish
Pages (from-to)1233-1261
Number of pages29
JournalAnnals of Statistics
Issue number4
Publication statusPublished - 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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