• Title, Summary, Keyword: empirical LIL

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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.

LIL FOR KERNEL ESTIMATOR OF ERROR DISTRIBUTION IN REGRESSION MODEL

  • Niu, Si-Li
    • Journal of the Korean Mathematical Society
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    • v.44 no.4
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    • pp.835-844
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    • 2007
  • This paper considers the problem of estimating the error distribution function in nonparametric regression models. Sufficient conditions are given under which the kernel estimator of the error distribution function based on nonparametric residuals satisfies the law of iterated logarithm.