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Random clouds and an application to censoring in survival analysis

Author

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  • Ivanoff, B.G.B. Gail
  • Merzbach, Ely

Abstract

The theory of optional stopping is extended from stopping sets to general adapted random sets called 'clouds' and 'anti-clouds', and a stopping theorem is proven for set-indexed martingales. An application to set-indexed survival analysis is given when the data points are indexed by sets and censored very generally by clouds. This type of censoring corresponds to filtering of survival data on R+. A Nelson-Aalen estimator is defined, and shown to be consistent and asymptotically unbiased.

Suggested Citation

  • Ivanoff, B.G.B. Gail & Merzbach, Ely, 2004. "Random clouds and an application to censoring in survival analysis," Stochastic Processes and their Applications, Elsevier, vol. 111(2), pages 259-279, June.
    • Handle: RePEc:eee:spapps:v:111:y:2004:i:2:p:259-279
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    Cited by:

    1. Carabarin-Aguirre, Alberto & Ivanoff, B. Gail, 2010. "Estimation of a distribution under generalized censoring," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1501-1519, July.

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