A note on nonparametric estimators of the bivariate survival function under univariate censoring

A simple nonparametric estimator is proposed for the underlying bivariate distribution of paired failure times in the presence of univariate right-censoring. The estimator is shown to be a particular path-dependent estimator which is a generalisation of an estimator proposed by Campbell & Foldes (1982). Under univariate censoring, this path-dependent estimator has the smallest variance among all path-dependent estimators, which includes the estimator proposed by Lin & Ying (1993).