Calibrated interpolated confidence intervals for population quantiles

Abstract

Beran & Hall's (1993) simple linear interpolation provides a very convenient approach for constructing nonparametric confidence intervals for population quantiles based on a random sample of size n. We show that the coverage error of the interpolated interval, which is of order O(n -1), can be improved upon by calibrating the nominal coverage level. Three distinct methods of calibration are considered. The analytical and Monte Carlo methods succeed in reducing the order of coverage error to O(n -3/2), while the smoothed bootstrap method reduces it further to O(n-25/14). We provide guidelines for practical implementation of the calibration methods. Their performance is compared with the simple linear interpolated interval in a simulation study which confirms superiority of the calibrated intervals. © 2005 Biometrika Trust.