• Title, Summary, Keyword: sequential Kaplan-Meier integral process

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THE EMPIRICAL LIL FOR THE KAPLAN-MEIER INTEGRAL PROCESS

  • Bae, Jong-Sig;Kim, Sung-Yeun
    • Bulletin of the Korean Mathematical Society
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    • v.40 no.2
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    • pp.269-279
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    • 2003
  • 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.