Kaplan-Meier Estimator under Association
Consider a long term study, where a series of possibly censored failure times is observed. Suppose the failure times have a common marginal distribution functionF, but they exhibit a mode of dependence characterized by positive or negative association. Under suitable regularity conditions, it is shown that the Kaplan-Meier estimatorFnofFis uniformly strongly consistent; rates for the convergence are also provided. Similar results are established for the empirical cumulative hazard rate function involved. Furthermore, a stochastic process generated byFnis shown to be weakly convergent to an appropriate Gaussian process. Finally, an estimator of the limiting variance of the Kaplan-Meier estimator is proposed and it is shown to be weakly convergent.
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Volume (Year): 67 (1998)
Issue (Month): 2 (November)
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