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.

翻译：众所周知，在异质性条件下，样本分位数的渐近方差相对于独立同分布情形可以降低。然而，目前尚无可用的渐近正确分位数置信区间。我们提出了一种新颖且一致的估计量，用于估计当分位数由观测组计算时所产生的缩减渐近方差，从而得到渐近正确的置信区间。模拟研究表明，我们的置信区间比独立同分布情形下的置信区间显著更短，并在广泛的异质设置下实现了近乎正确的覆盖率。