Product-limit estimators of the survival function with twice censored data
Valentin Patilea, Jean-Marie Rolin
The Annals of Statistics · 2006 · Volume 34 · Issue 2
DOI: 10.1214/009053606000000065
Abstract
A model for competing (resp. complementary) risks survival data where the failure time can be left (resp. right) censored is proposed. Product-limit estimators for the survival functions of the individual risks are derived. We deduce the strong convergence of our estimators on the whole real half-line without any additional assumptions and their asymptotic normality under conditions concerning only the observed distribution. When the observations are generated according to the double censoring model introduced by Turnbull, the product-limit estimators represent upper and lower bounds for Turnbull’s estimator.
Keywords
62G05, 62N01, 62N02, competing and complementary risks, delta-method, hazard functions, product-limit estimator, strong convergence, Twice censoring, weak convergence
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