A note on the asymptotic properties of the product-limit estimator on the whole line

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Abstract

It was shown by Gill (1983) that a Donsker type theorem for empirical distributions holds for Kaplan-Meier estimates up to the point of last observation. In this note, we show that this restriction to last observation is unnecessary and convergence holds on the entire interval, providing a full extension of Donsker's result to censored models.

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Cited by (31)

  • On the strong convergence of the product-limit estimator and its integrals under censoring and random truncation

    2000, Statistics and Probability Letters
    Citation Excerpt :

    A delicate part of the investigation is the proof of convergence near the boundaries of the support of F. For right-censored data, the uniform weak consistency of Fn over the entire interval was established by Gill (1983) for continuous F. The result has been extended by Wang (1987), Ying (1989) to an arbitrary F and the maximum order statistics. The uniform strong consistency was proved by Stute and Wang (1993) and simplified by Gill (1994).

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