Bulletin of the Korean Mathematical Society (대한수학회보)
- Volume 40 Issue 2
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- Pages.269-279
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- 2003
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- 1015-8634(pISSN)
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- 2234-3016(eISSN)
DOI QR Code
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.
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References
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