Distribution-free Approximate Methods for Constructing Confidence Intervals for Quantiles

Quantile estimation is important for a wide range of applications. While point estimates based on one or two order statistics are common, constructing confidence intervals around them, however, is a more difficult problem. This paper has two goals. First, it surveys the numerous distribution-free methods for constructing approximate confidence intervals for quantiles. These techniques can be divided roughly into four categories: using a pivotal quantity, resampling, interpolation, and empirical likelihood methods. Second, a method based on the pivotal quantity that has received limited attention in the past is extended. Comprehensive simulation studies are used to compare performance across methods. The proposed method is simple and performs similarly to linear interpolation methods and a smoothed empirical likelihood method. While the proposed method has slightly wider interval widths, it can be calculated for more extreme quantiles even when there are few observations.