Laws of the iterated logarithm for censored data

First- and second-order laws of the iterated logarithm are obtained for bot h the Nelson-Aalen and the Kaplan-Meier estimators in the random censorship model, uniform up to a large order statistic of the censored data. The rat es for the first-order processes are exact except for constants. The LIL fo r the second-order processes (where one subtracts a linear, empirical proce ss, term from the difference between the original process and the estimator ), uniform over fixed intervals, is also proved. Somewhat surprisingly, the re is a certain degree of proof unification for fixed and variable interval s in the second-order results for the Nelson-Aalen estimator. No assumption s are made on the distribution of the censoring variables and only continui ty of the distribution function of the original variables is assumed for th e results on the Kaplan-Meier estimator.