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On negative mass assigned by the bivariate Kaplan-Meier estimator. (English) Zbl 0738.62049
Summary: Conditions under which the bivariate Kaplan-Meier estimate of D. M. Dabrowska [ibid. 16, No. 4, 1475-1489 (1988; Zbl 0653.62071)] 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 \(n\to\infty\), 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.

MSC:
62G07 Density estimation
62H12 Estimation in multivariate analysis
62H10 Multivariate distribution of statistics
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