Product-Limit Estimators of the Survival Function with Twice Censored Data

A model for competing (resp. complementary) risks survival data where the failure time can beleft (resp. right) censored is proposed. Product-limit estimators for the survival functions of theindividual risks are derived. We deduce the strong convergence of our estimators on the wholereal half-line without any additional assumption and their asymptotic normality underconditions concerning only the observed distribution. When the observations are generatedaccording to the double censoring model introduced by Turnbull (1974), the product-limitestimators represent upper and lower bounds for Turnbull's estimator.