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Efficient estimation from right-censored data when failure indicators are missing at random. (English) Zbl 0932.62040
Summary: The Kaplan-Meier estimator of a survival function is well known to be asymptotically efficient when cause of failure is always observed. It has been an open problem, however, to find an efficient estimator when failure indicators are missing at random. S. H. Lo [J. Multivariate Anal. 39, No. 2, 217-235 (1991; Zbl 0741.62038)] showed that nonparametric maximum likelihood estimators are inconsistent and this has led to several proposals of ad hoc estimators, none of which are efficient.
We now introduce a sieved nonparametric maximum likelihood estimator, and show that it is efficient. Our approach is related to the estimation of a bivariate survival function from bivariate right-censored data.

MSC:
62G05 Nonparametric estimation
62N01 Censored data models
62N02 Estimation in survival analysis and censored data
62F12 Asymptotic properties of parametric estimators
62P10 Applications of statistics to biology and medical sciences; meta analysis
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