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The uniform law of large numbers for the Kaplan-Meier integral process

Published online by Cambridge University Press:  17 April 2009

Jongsig Bae  and
Sungyeun Kim
Jongsig Bae
Affiliation:
Department of Mathematics and Institute of Basic Science, SungKyunKwan University, Suwon 440–746, Korea e-mail: jsbae@yurim.skku.ac.kr, sykim@math.skku.ac.kr
Sungyeun Kim
Affiliation:
Department of Mathematics and Institute of Basic Science, SungKyunKwan University, Suwon 440–746, Korea e-mail: jsbae@yurim.skku.ac.kr, sykim@math.skku.ac.kr
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Abstract

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Let be the function-indexed Kaplan-Meier integral process constructed from the random censorship model. We study a uniform version of the law of large numbers of Glivenko-Cantelli type for {Un} under the bracketing entropy condition. The main result is that the almost sure convergence and convergence in the mean of the process Un holds uniformly in ℱ. In proving the result we shall employ the bracketing method which is used in the proof of the uniform law of large numbers for the complete data of the independent and identically distributed model.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 67 , Issue 3 , June 2003 , pp. 459 - 465
Copyright
Copyright © Australian Mathematical Society 2003

References

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