Universal Gaussian approximations under random censorship

Abstract

Universal Gaussian approximations are established for empirical cumulative hazard and product-limit processes under random censorship. They hold uniformly up to some large order statistics in the sample, with the approximation rates depending on the order of these statistics, and require no assumptions on the censoring mechanism. Weak convergence results and laws of the iterated logarithm follow on the whole line if the respective processes are stopped at certain large order statistics, depending on the type of result. Some new consequences and negative results for confidence-band construction are discussed. Some new uniform consistency rates up to large order statistics are also derived and shown to be universally best possible for a wide range of tail order statistics.