## The Annals of Statistics

### Confidence tubes for multiple quantile plots via empirical likelihood

#### Abstract

The nonparametric empirical likelihood approach is used to obtain simultaneous confidence tubes for multiple quantile plots based on $k$ independent (possibly right-censored) samples. These tubes are asymptotically distribution free, except when both $k \geq 3$ and censoring is present. Pointwise versions of the confidence tubes, however, are asymptotically distribution free in all cases. The various confidence tubes are valid under minimal conditions. The proposed methods are applied in three real data examples.

#### Article information

Source
Ann. Statist., Volume 27, Number 4 (1999), 1348-1367.

Dates
First available in Project Euclid: 4 April 2002

https://projecteuclid.org/euclid.aos/1017938929

Digital Object Identifier
doi:10.1214/aos/1017938929

Mathematical Reviews number (MathSciNet)
MR1740108

Zentralblatt MATH identifier
0957.62038

Subjects
Primary: 62G15: Tolerance and confidence regions
Secondary: 62G20: Asymptotic properties

#### Citation

Einmahl, John H. J.; McKeague, Ian W. Confidence tubes for multiple quantile plots via empirical likelihood. Ann. Statist. 27 (1999), no. 4, 1348--1367. doi:10.1214/aos/1017938929. https://projecteuclid.org/euclid.aos/1017938929

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• EINDHOVEN UNIVERSITY OF TECHNOLOGY TALLAHASSEE, FLORIDA 32306-4330 P.O. BOX 513 E-MAIL: mckeague@stat.fsu.edu 5600 MB EINDHOVEN THE NETHERLANDS E-MAIL: einmahl@win.tue.nl