Weak asymptotic representations for quantiles of the product-limit estimator

Abstract

Sufficient conditions are given under which quantiles Image of the product-limit estimator allow a Bahadur-type representation with remainder term op(n−1/2). Here {pn} is either a deterministic or random sequence. This weak representation theorem and a uniform version of it lead to first-order asymptotic results in the estimation theory for quantiles of the lifetime distribution and of the residual lifetime distribution.