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Product-limit Estimators of the Survival Function with Left or Right Censored Data

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  • Valentin Patilea

    (Crest)

  • Jean-Marc Rolin

    (Crest)

Abstract

The problem of estimating the distribution of a lifetime when data may be leftor right censored is considered. Two models are introduced and the correspondingproduct-limit estimators are derived. Strong uniform convergence and asymptoticnormality are proved for the product-limit estimators on the whole range of theobservations. A bootstrap procedure that can be applied to con¯dence intervalsconstruction is proposed.

Suggested Citation

  • Valentin Patilea & Jean-Marc Rolin, 2004. "Product-limit Estimators of the Survival Function with Left or Right Censored Data," Working Papers 2004-36, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2004-36
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    References listed on IDEAS

    as
    1. Jong S. Kim, 2003. "Maximum likelihood estimation for the proportional hazards model with partly interval‐censored data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 489-502, May.
    2. Rolin, J.M., 2001. "Nonparametric Competing Risks Models : Identification and Strong Consistency," Papers 0115, Catholique de Louvain - Institut de statistique.
    3. 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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