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Functional central limit theorems for the Nelson–Aalen and Kaplan–Meier estimators for dependent stationary data

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  • Anevski, Dragi

Abstract

We derive process limit distribution results for the Nelson–Aalen estimator of a hazard function and for the Kaplan–Meier estimator of a distribution function, under different dependence assumptions. The data are assumed to be right censored observations of a stationary time series. We treat weakly dependent as well as long range dependent data, and allow for qualitative differences in the dependence for the censoring times versus the time of interest.

Suggested Citation

  • Anevski, Dragi, 2017. "Functional central limit theorems for the Nelson–Aalen and Kaplan–Meier estimators for dependent stationary data," Statistics & Probability Letters, Elsevier, vol. 124(C), pages 83-91.
    • Handle: RePEc:eee:stapro:v:124:y:2017:i:c:p:83-91
    DOI: 10.1016/j.spl.2017.01.005
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    References listed on IDEAS

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    1. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, October.
    2. Sun, Liuquan & Zhou, Xian, 2001. "Survival function and density estimation for truncated dependent data," Statistics & Probability Letters, Elsevier, vol. 52(1), pages 47-57, March.
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