The nonparametric minimax estimation of an analytic density at a given point, under random censorship, is considered. Although the problem of estimating density is known to be irregular in a certain sense, we make some connections relating this problem to the problem of estimating smooth functionals. Under condition that the censoring is not too severe, we establish the exact limiting behavior ...

In some long term studies, a series of dependent and possibly censored failure times may be observed. Suppose that the failure times have a common marginal distribution function, and inferences about it are of our interest. The main result of this paper is that of providing, under certain regularity conditions, the Kaplan-Meier estimator can be expressed as the mean of random variables, with a ...