Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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THE EMPIRICAL LIL FOR THE KAPLAN-MEIER INTEGRAL PROCESS

  • Bae, Jong-Sig (Department of Mathematics, SungKyunKwan University) ;
  • Kim, Sung-Yeun (Department of Mathematics, SungKyunKwan University)
  • Published : 2003.05.01

Abstract

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 [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 result 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.

Keywords

Kaplan-Meier integral process;empirical LIL;sequential Kaplan-Meier integral process;empirical CLT;Gaussian process

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References

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