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.
The research of the second author was supported by grants RFBR 02-01-00262, grant RFBR-DFG 04-01-04000
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Huber, C., Solev, V., Vonta, F. (2006). Estimation Of Density For Arbitrarily Censored And Truncated Data. In: Nikulin, M., Commenges, D., Huber, C. (eds) Probability, Statistics and Modelling in Public Health. Springer, Boston, MA. https://doi.org/10.1007/0-387-26023-4_16
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DOI: https://doi.org/10.1007/0-387-26023-4_16
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