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We prove an empirical LIL for the Kaplan-Meier inte- gral process constructed from the random censorship model under bracketing entropy and mild assumptions due to censoring eects. The main method in deriving the empirical LIL is to use a weak convergence result of the sequential Kaplan-Meier integral process whose proofs appear in Bae and Kim (2). Using the result of weak convergence, we translate the problem of the Kaplan Meier integral process into that of a Gaussian process. Finally we derive the re- sult using an empirical LIL for the Gaussian process of Pisier (6) via a method adapted from Ossiander (5). The result of this paper extends the empirical LIL for IID random variables to that of a random censorship model.

THE EMPIRICAL LIL FOR THE KAPLAN-MEIER INTEGRAL PROCESS