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The Probability That the Largest Observation Is Censored
R. A. Maller and S. Zhou
Journal of Applied Probability
Vol. 30, No. 3 (Sep., 1993), pp. 602-615
Published by: Applied Probability Trust
Stable URL: http://www.jstor.org/stable/3214769
Page Count: 14
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Suppose n possibly censored survival times are observed under an independent censoring model, in which the observed times are generated as the minimum of independent positive failure and censor random variables. A practical difficulty arises when the largest observation is censored since then the usual non-parametric estimator of the distribution of the survival time is improper. We calculate the probability that this occurs and give necessary and sufficient conditions for this probability to converge to 0 as n→∞. As an application, we show that if this probability is 0, asymptotically, then a consistent estimator for the mean failure time can be found. An almost sure version of the problem is also considered.
Journal of Applied Probability © 1993 Applied Probability Trust