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March, 1991 Coverage Probabilities of Bootstrap-Confidence Intervals for Quantiles
Michael Falk, Edgar Kaufmann
Ann. Statist. 19(1): 485-495 (March, 1991). DOI: 10.1214/aos/1176347995


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.


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Michael Falk. Edgar Kaufmann. "Coverage Probabilities of Bootstrap-Confidence Intervals for Quantiles." Ann. Statist. 19 (1) 485 - 495, March, 1991.


Published: March, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0725.62043
MathSciNet: MR1091864
Digital Object Identifier: 10.1214/aos/1176347995

Primary: 62G15
Secondary: 62G30

Keywords: Bootstrap estimate , Confidence interval , Sample $q$-quantile

Rights: Copyright © 1991 Institute of Mathematical Statistics

Vol.19 • No. 1 • March, 1991
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