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August 2014 A second-order efficient empirical Bayes confidence interval
Masayo Yoshimori, Partha Lahiri
Ann. Statist. 42(4): 1233-1261 (August 2014). DOI: 10.1214/14-AOS1219

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.

Citation

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Masayo Yoshimori. Partha Lahiri. "A second-order efficient empirical Bayes confidence interval." Ann. Statist. 42 (4) 1233 - 1261, August 2014. https://doi.org/10.1214/14-AOS1219

Information

Published: August 2014
First available in Project Euclid: 25 June 2014

zbMATH: 1297.62019
MathSciNet: MR3226156
Digital Object Identifier: 10.1214/14-AOS1219

Subjects:
Primary: 62C12
Secondary: 62F25

Keywords: Adjusted maximum likelihood , coverage error , Empirical Bayes , linear mixed model

Rights: Copyright © 2014 Institute of Mathematical Statistics

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Vol.42 • No. 4 • August 2014
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