Bahadur-Kiefer theorems for the product-limit process

Abstract

In the random censorship from the right model, strong and weak limit theorems for Bahadur-Kiefer type processes based on the product-limit estimator are established. The main theorm is sharp and may be considered as a final result as far as this type of research is concerned. As a consequence of this theorem a sharp uniform Bahadur representation for product-limit quantiles is obtained.Bahadur representation empirical and quantile processes limit theorems product-limit random censorship