Nonparametric estimation of a bivariate survivorship function with doubly censored data

The problem of nonparametric estimation of a bivariate survivorship function with doubly censored data is considered. A self-consistent estimator is developed by first "reducing" the problem to that of estimation in a singly and right censored situation. This estimator is shown to satisfy a likelihood equation, and its uniqueness is investigated. The results obtained naturally parallel those obtained by Campbell (1981) in the singly censored case.