We consider nonparametric estimation in 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 $0$ of the unknown distribution function $F$ of the ball-squared radii. We prove a corresponding local asymptotic minimax lower bound, as well under some local smoothness condition. This solves in an adaptive way the nonparametric estimation problem.
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