Abstract
We propose and analyze a new estimator of a survival function in the random censorship model when the censoring indicator is missing at random for some study subjects. The proposed approach appeals to a known representation for the survival function, expressible as a smooth functional of a certain conditional probability and the cumulative hazard function of the observed minimum. Well-known estimators are substituted into this representation leading to a simple estimator of the survival function. The new estimator, whose asymptotic variance reduces to that of the Kaplan-Meier estimator when all the censoring indicators are observed, is shown to achieve the efficiency bound derived by van der Laan and McKeague.
Original language | English (US) |
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Pages (from-to) | 797-817 |
Number of pages | 21 |
Journal | Journal of Nonparametric Statistics |
Volume | 16 |
Issue number | 5 |
DOIs | |
State | Published - Oct 2004 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
Keywords
- Bandwidth sequence
- Kernel density estimator
- Limit theory
- Mean integrated squared error
- Reduced-data nonparametric maximum likelihood estimator
- U-statistic