The Annals of Statistics

A second-order efficient empirical Bayes confidence interval

Masayo Yoshimori and Partha Lahiri

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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.

Article information

Ann. Statist., Volume 42, Number 4 (2014), 1233-1261.

First available in Project Euclid: 25 June 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62C12: Empirical decision procedures; empirical Bayes procedures
Secondary: 62F25: Tolerance and confidence regions

Adjusted maximum likelihood coverage error empirical Bayes linear mixed model


Yoshimori, Masayo; Lahiri, Partha. A second-order efficient empirical Bayes confidence interval. Ann. Statist. 42 (2014), no. 4, 1233--1261. doi:10.1214/14-AOS1219.

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