Identifiability and censored data

Nader Ebrahimi

Biometrika, 2003, vol. 90, issue 3, 724-727

Abstract: It is well known that, without the assumption of independence between two nonnegative random variables X and Y, the survival function of X is not identifiable on the basis of the joint distribution function of Z = min(X, Y) and &dgr; = I(Z = Y). In this paper, we provide a simple condition in the form of conditional distribution of Y given X. We show that our condition is equivalent to the constant-sum condition proposed by Williams & Lagakos (1977). As a result the survival function of X can be identified from the joint distribution of Z and &dgr; and the Kaplan--Meier estimator with Greenwood's formula for its variance remains valid. Examples which satisfy the condition are given. Copyright Biometrika Trust 2003, Oxford University Press.

Date: 2003
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