## The Annals of Statistics

### Coverage Probabilities of Bootstrap-Confidence Intervals for Quantiles

#### Abstract

An asymptotic expansion of length 2 is established for the coverage probabilities of confidence intervals for the underlying $q$-quantile which are derived by bootstrapping the sample $q$-quantile. The corresponding level error turns out to be of order $O(n^{-1/2})$ which is unexpectedly low. A confidence interval of even more practical use is derived by using backward critical points. The resulting confidence interval is of the same length as the one derived by ordinary bootstrap but it is distribution free and has higher coverage probability.

#### Article information

Source
Ann. Statist., Volume 19, Number 1 (1991), 485-495.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347995

Digital Object Identifier
doi:10.1214/aos/1176347995

Mathematical Reviews number (MathSciNet)
MR1091864

Zentralblatt MATH identifier
0725.62043

JSTOR
links.jstor.org

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

#### Citation

Falk, Michael; Kaufmann, Edgar. Coverage Probabilities of Bootstrap-Confidence Intervals for Quantiles. Ann. Statist. 19 (1991), no. 1, 485--495. doi:10.1214/aos/1176347995. https://projecteuclid.org/euclid.aos/1176347995