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Kaplan-Meier Estimator under Association

Listed author(s):
  • Cai, Zongwu
  • Roussas, George G.

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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Article provided by Elsevier in its journal Journal of Multivariate Analysis.

Volume (Year): 67 (1998)
Issue (Month): 2 (November)
Pages: 318-348

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Handle: RePEc:eee:jmvana:v:67:y:1998:i:2:p:318-348
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  1. Stute, Winfried, 1994. "Convergence of the Kaplan-Meier estimator in weighted sup-norms," Statistics & Probability Letters, Elsevier, vol. 20(3), pages 219-223, June.
  2. Roussas, G. G., 1994. "Asymptotic Normality of Random Fields of Positively or Negatively Associated Processes," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 152-173, July.
  3. Roussas, George G., 1991. "Kernel estimates under association: strong uniform consistency," Statistics & Probability Letters, Elsevier, vol. 12(5), pages 393-403, November.
  4. Ying, Z. & Wei, L. J., 1994. "The Kaplan-Meier Estimate for Dependent Failure Time Observations," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 17-29, July.
  5. Bagai, Isha & Prakasa Rao, B. L. S., 1991. "Estimation of the survival function for stationary associated processes," Statistics & Probability Letters, Elsevier, vol. 12(5), pages 385-391, November.
  6. Burton, Robert M. & Dabrowski, AndréRobert & Dehling, Herold, 1986. "An invariance principle for weakly associated random vectors," Stochastic Processes and their Applications, Elsevier, vol. 23(2), pages 301-306, December.
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