Asymptotic Distribution of the Kaplan–Meier U-Statistics

Consider the Kaplan–Meier estimate of the distribution function for right randomly censored data. We show that a U-statistic defined via this estimate is asymptotically normal. Under a condition of degeneracy, different from the degeneracy condition in uncensored models, it has an asymptotic nonnorm...

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Veröffentlicht in:	Journal of multivariate analysis 2002-10, Vol.83 (1), p.84-123
Hauptverfasser:	Bose, Arup, Sen, Arusharka
Format:	Artikel
Sprache:	eng
Schlagworte:	Applications central limit theorem degenerate U-statistics Distribution theory double Wiener integral Exact sciences and technology Kaplan–Meier integral law of iterated logarithm Mathematics Nonparametric inference Parametric inference Probability and statistics random censoring random censoring Kaplan-Meier integral U-statistics central limit theorem law of iterated logarithm degenerate U-statistics double Wiener integral Reliability, life testing, quality control Sciences and techniques of general use Statistics U-statistics
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Beschreibung
Zusammenfassung:	Consider the Kaplan–Meier estimate of the distribution function for right randomly censored data. We show that a U-statistic defined via this estimate is asymptotically normal. Under a condition of degeneracy, different from the degeneracy condition in uncensored models, it has an asymptotic nonnormal distribution.
ISSN:	0047-259X 1095-7243
DOI:	10.1006/jmva.2001.2039