Quantile residual lifetime for left-truncated and right-censored data

This article proposes a simple nonparametric estimator of quantile residual lifetime function under left-truncated and right-censored data. The asymptotic consistency and normality of this estimator are proved and the variance expression is calculated. Two bootstrap procedures are employed in the simulation study, where the latter bootstrap from Zeng and Lin (2008) is 4000 times faster than the former naive one, and the numerical results in both methods show that our estimating approach works well. A real data example is used to illustrate its application.