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Kaplan–Meier Estimator under Association

Authors
Journal
Journal of Multivariate Analysis
0047-259X
Publisher
Elsevier
Publication Date
Volume
67
Issue
2
Identifiers
DOI: 10.1006/jmva.1998.1769
Keywords
  • Censored Data
  • Kaplan–Meier Estimator
  • Negative Association
  • Positive Association
  • Strong Consistency
  • Variance Estimator
  • Weak Convergence
Disciplines
  • Mathematics

Abstract

Abstract Consider a long term study, where a series of possibly censored failure times is observed. Suppose the failure times have a common marginal distribution function F, but they exhibit a mode of dependence characterized by positive or negative association. Under suitable regularity conditions, it is shown that the Kaplan–Meier estimator F n of Fis 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 by F n is 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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