UNIVERSAL GAUSSIAN APPROXIMATIONS UNDER RANDOM CENSORSHIP

Universal Gaussian approximations are established for empirical cu mul ative 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, an d 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 statistic s, depending on the type of result. Some new consequences and negative results for confidence-band construction are discussed. Some new unif orm consistency rates up to large order statistics are also derived an d shown to be universally best possible for a wide range of tail order statistics.