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Product-Limit Estimators of the Survival Function with Twice Censored Data

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  • Valentin Patilea

    (Crest)

  • Jean-Marie Rolin

    (Crest)

Abstract

A model for competing (resp. complementary) risks survival data where the failure time can beleft (resp. right) censored is proposed. Product-limit estimators for the survival functions of theindividual risks are derived. We deduce the strong convergence of our estimators on the wholereal half-line without any additional assumption and their asymptotic normality underconditions concerning only the observed distribution. When the observations are generatedaccording to the double censoring model introduced by Turnbull (1974), the product-limitestimators represent upper and lower bounds for Turnbull's estimator.

Suggested Citation

  • Valentin Patilea & Jean-Marie Rolin, 2004. "Product-Limit Estimators of the Survival Function with Twice Censored Data," Working Papers 2004-05, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2004-05
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    References listed on IDEAS

    as
    1. Rolin, J.M., 2001. "Nonparametric Competing Risks Models : Identification and Strong Consistency," Papers 0115, Catholique de Louvain - Institut de statistique.
    2. Ying, Zhiliang, 1989. "A note on the asymptotic properties of the product-limit estimator on the whole line," Statistics & Probability Letters, Elsevier, vol. 7(4), pages 311-314, February.
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