Efficient Estimation for Censored Quantile Regression

Censored quantile regression (CQR) has received growing attention in survival analysis because of its flexibility modeling heterogeneous effect covariates. Advances have been made developing various inferential procedures under different assumptions and settings. Under the conditional independence assumption, many existing CQR methods can be characterized either by stochastic integral-based estimating equations (see, e.g., Peng Huang) or locally weighted approaches to adjust for censored observations instance, Wang Wang). While there proposals apparently dissimilar strategies terms formulations techniques applied CQR, inter-relationships amongst these are rarely discussed literature. In addition, given complicated structure asymptotic variance, limited investigation on improving estimation efficiency models. This article addresses open questions proposing a unified framework which conventional covered as special cases. The new formulation also facilitates construction most efficient estimator parameters interest general class functions. Asymptotic properties including consistency weak convergence proposed established via martingale-based argument. Numerical studies presented illustrate promising performance compared contenders Supplementary materials this available online.