Resampling-based Inference Procedure for Median Regression Estimator with Censored Data

Quantile regression has become increasingly popular across various disciplines due to its robustness, offering an alternative to traditional mean-based regression. Unlike traditional linear regression, quantile regression estimates conditional quantiles, capturing the full complexity of the relationships between variables (specifically, the conditional dependence of lifetime on covariates in lifetime analysis). However, inference procedures in quantile regression often involve complex non-parametric methods, as the variance of an estimator typically depends on the unknown error density, making it difficult to estimate. In this paper, we present a bootstrap-type resampling method that simplifies the construction of the inference procedures using the censored median regression estimator originally proposed by Yang (1999). Numerical simulations are performed to validate the proposed procedures.