A New Nonparametric Empirical Likelihood Estimator for Quantile Regression under Right Censoring

In this paper, we propose a new nonparametric empirical likelihood (EL) method for estimating conditional quantile functions in the presence of right-censored data. Quantile regression offers a flexible alternative to mean regression by capturing heterogeneous covariate effects across the conditional distribution of the response variable. However, right censoring poses substantial challenges for estimation and inference. Our approach combines empirical likelihood with inverse probability of censoring weighting (IPCW) and kernel smoothing techniques to construct a fully nonparametric estimator of conditional quantile functions. The proposed method avoids strong parametric assumptions and enables likelihood-based inference, yielding asymptotically valid confidence intervals without requiring explicit variance estimation. We establish theoretical properties including consistency and asymptotic normality. Simulation studies illustrate the finite-sample performance of the proposed method under several scenarios, and an application to real survival data illustrates the practical utility of the proposed method.