Modified EM-estimator of the Bivariate Survival Function

Pruitt (1991b) proposed estimating a bivariate survival function for censored data by modifying the self-consistency equations of the EM-algorithm. Though not efficient, the estimator has very good practical performance. In this paper, we prove weak convergence at √ n-rate, strong uniform consistency and a semiparametric bootstrap result for this implicitly defined estimator. The estimator is analyzed by application of the implicit function theorem. Because the estimator uses kernel density estimators, part of the analysis is concerned with proving root-n weak convergence of functionals of density estimators. We consider this problem in generality and show that the functional delta-method (Gill, 1989, van der Vaart and Wellner, 1993) can be refined to this case.