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

Jean-Yves Dauxois

Stochastic Processes and their Applications, 2000, vol. 90, issue 2, 327-334

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.

Keywords: Stochastic; integral; Counting; process; Martingale; Weak; convergence; Censored; data; Product; integral; Gaussian; process (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (2)

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