Weak and strong quantile representations for randomly truncated data with applications

Abstract

Suppose that we observe bivariate data (X,. q) only when Y, < Xi (left truncation). Denote with F the marginal d.f. of the X’s In this paper we derive a Bahadur-type representation for the quantile function of the pertaining product-limit estimator of F. As an application we obtain confidence intervals and bands for quantiles of F.