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September, 1993 Smoothed Empirical Likelihood Confidence Intervals for Quantiles
Song Xi Chen, Peter Hall
Ann. Statist. 21(3): 1166-1181 (September, 1993). DOI: 10.1214/aos/1176349256

Abstract

Standard empirical likelihood confidence intervals for quantiles are identical to sign-test intervals. They have relatively large coverage error, of size $n^{-1/2}$, even though they are two-sided intervals. We show that smoothed empirical likelihood confidence intervals for quantiles have coverage error of order $n^{-1}$, and may be Bartlett-corrected to produce intervals with an error of order only $n^{-2}$. Necessary and sufficient conditions on the smoothing parameter, in order for these sizes of error to be attained, are derived. The effects of smoothing on the positions of endpoints of the intervals are analysed, and shown to be only of second order.

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Song Xi Chen. Peter Hall. "Smoothed Empirical Likelihood Confidence Intervals for Quantiles." Ann. Statist. 21 (3) 1166 - 1181, September, 1993. https://doi.org/10.1214/aos/1176349256

Information

Published: September, 1993
First available in Project Euclid: 12 April 2007

zbMATH: 0786.62053
MathSciNet: MR1241263
Digital Object Identifier: 10.1214/aos/1176349256

Subjects:
Primary: 62G15
Secondary: 62G30

Rights: Copyright © 1993 Institute of Mathematical Statistics

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Vol.21 • No. 3 • September, 1993
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