Quantile regression with doubly censored data

Quantile regression offers a semiparametric approach to modeling data with possible heterogeneity. It is particularly attractive for censored responses, where the conditional mean functions are unidentifiable without parametric assumptions on the distributions. A new algorithm is proposed to estimate the regression quantile process when the response variable is subject to double censoring. The algorithm distributes the probability mass of each censored point to its left or right appropriately, and iterates towards self-consistent solutions. Numerical results on simulated data and an unemployment duration study are given to demonstrate the merits of the proposed method.