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.

中文翻译：

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构建分位数置信区间的无分布近似方法

分位数估算对于广泛的应用很重要。虽然基于一阶或二阶统计量的点估计很常见，但是围绕它们构建置信区间却是一个更加困难的问题。本文有两个目标。首先，它调查了许多用于构建分位数的近似置信区间的无分布方法。这些技术可以大致分为四类：使用枢轴数量，重采样，插值和经验似然方法。其次，扩展了基于过去很少受到关注的枢轴数量的方法。全面的仿真研究用于比较各种方法的性能。所提出的方法很简单，并且执行起来与线性插值方法和平滑的经验似然方法相似。