A New Approach to Censored Quantile Regression Estimation*

Quantile regression provides an attractive tool to the analysis of censored responses, because the conditional quantile functions are often of direct interest in regression analysis, and moreover, the quantiles are often identifiable while the conditional mean functions are not. Existing methods of estimation for censored quantiles are mostly limited to singly left- or right-censored data, with some attempts made to extend the methods to doubly-censored data. In this article we propose a new and unified approach, based on a variation of the data augmentation algorithm, to censored quantile regression estimation. The proposed method adapts easily to different forms of censoring including doubly censored and interval censored data, and somewhat surprisingly, the resulting estimates improve on the performance of the best known estimators with singly censored data.分位数回归（Quantile Regression）为删失响应的分析提供了极具吸引力的工具：在回归分析中，条件分位数函数往往具有直接的研究价值，且更为关键的是，分位数通常是可识别的，而条件均值函数则未必。现有删失分位数的估计方法大多仅局限于单向左删失或右删失数据，仅有少量研究尝试将此类方法拓展至双删失数据场景。本文基于数据增强（Data Augmentation）算法的一种变体，针对删失分位数回归估计问题提出了一种全新且统一的方法。所提方法可轻松适配多种删失形式，包括双删失与区间删失数据；且颇为意外的是，该方法得到的估计量性能优于现有针对单向删失数据的最优已知估计量。