## The Annals of Statistics

### Smoothed Empirical Likelihood Confidence Intervals for Quantiles

#### 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.

#### Article information

Source
Ann. Statist. Volume 21, Number 3 (1993), 1166-1181.

Dates
First available: 12 April 2007

http://projecteuclid.org/euclid.aos/1176349256

JSTOR

Digital Object Identifier
doi:10.1214/aos/1176349256

Mathematical Reviews number (MathSciNet)
MR1241263

Zentralblatt MATH identifier
0786.62053

Subjects
Primary: 62G15: Tolerance and confidence regions
Secondary: 62G30: Order statistics; empirical distribution functions

#### Citation

Chen, Song Xi; Hall, Peter. Smoothed Empirical Likelihood Confidence Intervals for Quantiles. The Annals of Statistics 21 (1993), no. 3, 1166--1181. doi:10.1214/aos/1176349256. http://projecteuclid.org/euclid.aos/1176349256.