An informative subset-based estimator for censored quantile regression

Quantile regression in the presence of fixed censoring has been studied extensively in the literature. However, existing methods either suffer from computational instability or require complex procedures involving trimming and smoothing, which complicates the asymptotic theory of the resulting estimators. In this paper, we propose a simple estimator that is obtained by applying standard quantile regression to observations in an informative subset. The proposed method is computationally convenient and conceptually transparent. We demonstrate that the proposed estimator achieves the same asymptotical efficiency as the Powell's estimator, as long as the conditional censoring probability can be estimated consistently at a nonparametric rate and the estimated function satisfies some smoothness conditions. A simulation study suggests that the proposed estimator has stable and competitive performance relative to more elaborate competitors.