Postprint version. Published in Statistics and Probability Letters, Volume 29, Issue 1, August 15, 1996, pages 45-53. Copyright © 1996 Elsevier. The definitive version is available at http://dx.doi.org/10.1016/0167-7152(95)00154-9.
NOTE: At the time of publication, the author Theodore P. Hill was not yet affiliated with Cal Poly.
Strongly-consistent, distribution-free confidence intervals are derived to estimate the fixed quantiles of an arbitrary unknown distribution, based on order statistics of an iid sequence from that distribution. This new method, unlike classical estimates, works for totally arbitrary (including discontinuous) distributions, and is based on recent one-sided strong laws of large numbers.