Nonparametric estimations of quantile residual life function with censored length-biased data

In biomedical studies, the median or quantile residual life is often treated as an important quantitative measure for the length of individuals' residual life besides the mean residual life. In this paper, two nonparametric estimating methods for quantile residual life function are developed with censored length-biased data, and they are constructed based on the moment-based estimation idea and martingale theory, respectively. In particular, the proposed martingale-based estimating method can avoid estimating the survival function of the target population or the right-censoring variable. The consistency and weak convergence of two estimations are also established. In order to evaluate their performance and accuracy in a finite sample, a series of small simulation studies are carried out, too. Finally, an analysis of the famous Channing House data is provided.