Nonparametric bivariate estimation with randomly censored data

The estimation of a bivariate distribution function with randomly censored data is considered. It is assumed that the censoring occurs independently of the lifetimes, and that deaths and losses which occur simultaneously can be separated. Two estimators are developed: a reduced-sample estimator and a self-consistent one. It is shown that the latter estimator satisfies a nonparametric likelihood function and is unique up to the final uncensored values in any dimension; it jumps at the points of double deaths in both dimensions.