Asymptotically local minimax estimation of infinitely smooth density with censored data

The problem of the nonparametric minimax estimation of an infinitely smooth density at a given point, under random censorship, is considered. We establish the exact asymptotics of the local minimax risk and propose the efficient kernel-type estimator based on the well known Kaplan-Meier estimator. Key words and phrases: Efficient estimator, local minimax risk, Kaplan-Meier estimator, kernel, random censorship