The rate of convergence of oscillation modules for product-limit process (Q1906612)

The global oscillation modulus of two classes of product limit estimators, Kaplan-Meier estimator and Lynden-Bell estimator, is investigated based on data which are subject to right censorship and left truncation. Sharp rates of convergence of the global oscillation modulus are established. These results parallel those of the uniform empirical process in the i.i.d. case. Some of the results are applied to get best rates of convergence for various types of density and hazard function estimators as well as error estimates for Bahadur representations of product-limit quantile estimators.