Quantile-Based Empirical Likelihood Inference on Median Residual Life Functions

The application of quantile-based empirical likelihood ratio tests to median residual life estimation in the presence of censored data is of great value. Unlike traditional methods that require variance estimation or having to depend on the distribution of the data, the proposed approach eliminates the complexity while retaining desirable statistical properties that the quantile-based empirical likelihood solution offers. The quantile-based empirical likelihood framework enables straightforward hypothesis testing and confidence interval construction for residual life distributions. We extend this methodology to the estimation of median residual lifetimes, providing a robust alternative to mean-based approaches, which can be problematic under censoring. We validated the proposed quantile-based empirical likelihood method through simulations and real-world data, confirming its effectiveness and superiority as a robust nonparametric tool for analyzing censored survival data