Tighter confidence intervals for quantiles of heterogeneous data

It is well known that the asymptotic variance of sample quantiles can be reduced under heterogeneity relative to the i.i.d. setting. However, asymptotically correct confidence intervals for quantiles are not yet available. We propose a novel, consistent estimator of the reduced asymptotic variance arising when quantiles are computed from groups of observations, leading to asymptotically correct confidence intervals. Simulation studies show that our confidence intervals are substantially shorter than those in the i.i.d. case and attain nearly correct coverage across a wide range of heterogeneous settings.