The empirical LIL for the Kaplan-Meier integral process

Abstract

process constructed from the random censorship model underbracketing entropy and mild assumptions due to censoring effects.The main method in deriving the empirical LIL is to use a weakconvergence result of the sequential Kaplan-Meier integral processwhose proofs appear in Bae and Kim cite{ReferBAEKIM}. Using theresult of weak convergence, we translate the problem of the KaplanMeier integral process into that of a Gaussian process. Finallywe derive the result using an empirical LIL for the Gaussianprocess of Pisier cite{ReferPIS} via a method adapted fromOssiander cite{ReferOS}. The result of this paper extends theempirical LIL for IID random variables to that of a randomcensorship model.