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The probability that the largest observation is censored

Part of: Distribution theory Limit theorems

Published online by Cambridge University Press:  14 July 2016

R. A. Maller  and
S. Zhou
R. A. Maller
Affiliation:
University of Western Australia
S. Zhou*
Affiliation:
University of Western Australia
*
∗ Postal address for both authors: Department of Mathematics, The University of Western Australia, Nedlands, WA 6009, Australia.
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Abstract

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.

Keywords

INDEPENDENT CENSORINGCONSISTENT ESTIMATIONMAXIMUM OF RANDOM VARIABLES

MSC classification

Primary: 60F05: Central limit and other weak theorems
Secondary: 60F15: Strong theorems 62E20: Asymptotic distribution theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 30 , Issue 3 , September 1993 , pp. 602 - 615
Copyright
Copyright © Applied Probability Trust 1993 

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