Bulletin of the
Korean Mathematical Society BKMS

We prove an empirical LIL for the Kaplan-Meier integral process constructed from the random censorship model under bracketing entropy and mild assumptions due to censoring effects. 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 \cite{ReferBAEKIM}. 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 result using an empirical LIL for the Gaussian process of Pisier \cite{ReferPIS} via a method adapted from Ossiander \cite{ReferOS}. The result of this paper extends the empirical LIL for IID random variables to that of a random censorship model.

Keywords: Kaplan-Meier integral process, empirical LIL, sequential Kaplan-Meier integral process, empirical CLT, Gaussian process

MSC numbers: Primary 60F15, 60F17; Secondary 60G42