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A new method for proving weak convergence results applied to nonparametric estimators in survival analysis

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  • Dauxois, Jean-Yves

Abstract

Using the limit theorem for stochastic integral obtained by Jakubowski et al. (Probab. Theory Related Fields 81 (1989) 111-137), we introduce in this paper a new method for proving weak convergence results of empirical processes by a martingale method which allows discontinuities for the underlying distribution. This is applied to Nelson-Aalen and Kaplan-Meier processes. We also prove that the same conclusion can be drawn for Hjort's nonparametric Bayes estimators of the cumulative distribution function and cumulative hazard rate.

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  • Dauxois, Jean-Yves, 2000. "A new method for proving weak convergence results applied to nonparametric estimators in survival analysis," Stochastic Processes and their Applications, Elsevier, vol. 90(2), pages 327-334, December.
    • Handle: RePEc:eee:spapps:v:90:y:2000:i:2:p:327-334
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    References listed on IDEAS

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    1. Jean-Yves Dauxois, 1998. "A New Method for Proving Weak Convergence Results Applied to Hjort’s Nonparametric Bayes Estimators," Working Papers 98-20, Center for Research in Economics and Statistics.
    2. repec:crs:wpaper:9820 is not listed on IDEAS
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    Cited by:

    1. Jean-Yves Dauxois & Agathe Guilloux, 2004. "Estimating the Cumulative incidence Functions under Length-biased Sampling," Working Papers 2004-01, Center for Research in Economics and Statistics.
    2. Jean-Yves Dauxois & Agathe Guilloux & Syed N. U. A. Kirmani, 2004. "Estimation in a Competing Risks Proportional Hazards Model Under Length-biased Sampling with Censoring," Working Papers 2004-02, Center for Research in Economics and Statistics.

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