Asymptotically efficient estimation in the Wicksell problem

Abstract

We consider the classical Wicksell problem of estimating an unknown distribution function $G$of the radii of balls, based on their observed crosssections. It is assumed that the underlying distribution function$G$ belongs to a Hölder class of smoothness $\gamma >1/2$. We prove that, for a suitable choice of the smoothing parameters, kernel-type estimators are asymptotically efficient for a large class of symmetric bowl-shaped loss functions.