Product-limit estimators of the survival function with twice censored data

Details Product-limit estimators of the survival function with twice censored data Product-limit estimators of the survival function with twice censored data

2006-07-03

arxiv.org/abs/math/0607036v1

Annals of Statistics 2006, Vol. 34, No. 2, 925-938

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053606000000065 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053606000000065

A model for competing (resp. complementary) risks survival data where the failure time can be left (resp. right) censored is proposed. Product-limit estimators for the survival functions of the individual risks are derived. We deduce the strong convergence of our estimators on the whole real half-line without any additional assumptions and their asymptotic normality under conditions concerning only the observed distribution. When the observations are generated according to the double censoring model introduced by Turnbull, the product-limit estimators represent upper and lower bounds for Turnbull's estimator.

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