Open Access
March, 1991 On Negative Mass Assigned by the Bivariate Kaplan-Meier Estimator
Ronald C. Pruitt
Ann. Statist. 19(1): 443-453 (March, 1991). DOI: 10.1214/aos/1176347992


Conditions under which the bivariate Kaplan-Meier estimate of Dabrowska is not a proper survival function are given. All points assigned negative mass are identified under the assumption that the observations follow an absolutely continuous distribution. The number of points assigned negative mass increases as $n^2$ and the total amount of negative mass does not disappear as $n \rightarrow \infty$, where $n$ is the sample size. A simulation study is reported which shows that large amounts of negative mass are assigned by the estimator, amounts ranging from 0.3 to 0.6 for a sample of size 50 over a variety of parameters for bivariate exponential distributions.


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Ronald C. Pruitt. "On Negative Mass Assigned by the Bivariate Kaplan-Meier Estimator." Ann. Statist. 19 (1) 443 - 453, March, 1991.


Published: March, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0738.62049
MathSciNet: MR1091861
Digital Object Identifier: 10.1214/aos/1176347992

Primary: 62H10
Secondary: 62G05

Keywords: Censored data , improper survival function

Rights: Copyright © 1991 Institute of Mathematical Statistics

Vol.19 • No. 1 • March, 1991
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