Quantiles of Kaplan-Meier Estimator.
STANFORD UNIV CA DEPT OF STATISTICS
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The theory of counting processes, martingales and stochastic integration is used to establish in a simple way a Bahadur representation for the quantiles of the Kaplan-Meier estimator. This Bahadur representation is combined with a result of Aalen 1976 to prove the asymptotic independence of the quantile estimates in the competing risks problem. Finally, the theory is used to study the estimates of the quantiles of the life length of a coherent system proposed by Doss, Freitag, and Proschan 1986. Keywords Quantiles competing risks problem Bahadur representation Kaplan Meier estimator coherent structure reliability function stochastic integral.
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