Interval censored and truncated data: Rate of convergence of NPMLE of the density |
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| Authors: | Catherine Huber Valentin Solev Filia Vonta |
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| Affiliation: | 1. Université René Descartes, Paris 5, 45 rue des Saints-Péres, 75006 Paris, France;2. Steklov Institute of Mathematics at St. Petersburg, nab. Fontanki, 27 St. Petersburg 191023, Russia;3. Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, CY-1678 Nicosia, Cyprus |
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| Abstract: | We consider survival data that are both interval censored and truncated. Under appropriate assumptions on the involved distributions, the censoring, truncation and survival, we prove the consistency of the NPMLE of the density of the survival, and give the rate of convergence. Finally, we give an example where the joint law of the censoring and truncation can be explicitly computed. |
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| Keywords: | Censored and truncated data Nonparametric maximum likelihood estimation Consistency Bracketing entropy Hellinger distance Rate of convergence |
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