## The Annals of Statistics

### A second-order efficient empirical Bayes confidence interval

#### 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 $O(m^{-{3}/{2}})$. 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

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

Dates
First available in Project Euclid: 25 June 2014

https://projecteuclid.org/euclid.aos/1403715200

Digital Object Identifier
doi:10.1214/14-AOS1219

Mathematical Reviews number (MathSciNet)
MR3226156

Zentralblatt MATH identifier
1297.62019

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

#### Citation

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. https://projecteuclid.org/euclid.aos/1403715200

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