Sequential confidence bands for quantile densities under truncated and censored data

In this paper an asymptotic distribution is obtained for the maximal deviation between the kernel quantile density estimator and the quantile density when the data are subject to random left truncation and right censorship. Based on this result we propose a fully sequential procedure for constructing a fixed-width confidence band for the quantile density on a finite interval and show that the procedure has the desired coverage probability asymptotically as the width of the band approaches zero.