Confidence bands for percentile residual lifetime under random censorship model

Abstract

Under the random censorship model from the right, we construct confidence bands for the (1 − p) percentile residual lifetime, R ( p) ( t) = Q(1 − p(1 − F 0( t))) − t, where F 0 and Q denote the distribution and quantile functions, respectively. We first prove that the scaled PL(1 − p) percentile residual lifetime process r n ( p) ( t) can be almost surely approximated by appropriate Gaussian processes which, however, depend on the unknown underlying distribution and quantile functions. This leads us to bootstrapping considerations. We define the bootstrapped PL(1 − p) percentile residual lifetime process and discuss approximations of this process by appropriate Gaussian processes. The latter enables us to construct bootstrapped confidence bands for R ( p) ( t).