Estimation Of Density For Arbitrarily Censored And Truncated Data

  • Catherine Huber
  • Valentin Solev
  • Filia Vonta
Conference paper

Summary

We consider survival data that are both interval censored and truncated. Turnbull [Tur76] proposed in 1976 a nice method for nonparametric maximum likelihood estimation of the distribution function in this case, which has been used since by many authors. But, to our knowledge, the consistency of the resulting estimate was never proved. We prove here the consistency of Turnbull’s NPMLE under appropriate conditions on the involved distributions: the censoring, truncation and survival distributions.

Key words

incomplete observations censored and truncated data nonparametric maximum likelihood estimation consistency 
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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Catherine Huber
    • 1
  • Valentin Solev
    • 2
  • Filia Vonta
    • 3
  1. 1.Université René Descartes - Paris 5Paris
  2. 2.Steklov Institute of MathematicsSt.PetersburgRussia
  3. 3.Department of Mathematics and StatisticsUniversity of CyprusNicosiaCyprus

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