Adaptive and Efficient Isotonic Estimation in Wicksell's Problem

Abstract

We consider the nonparametric estimation in the so-called Wicksell’s problem and we show that the isotonized version of the plug-in estimator is asymptotically efficient. The asymptotic variance will depend on the local smoothness at the estimation point and at zero of the unknown distribution function F of the ball squared radii. This solves in an adaptive way the nonparametric estimation problem.