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.

翻译：我们研究Wicksell问题中的非参数估计，并证明插入估计量的保序版本是渐近有效的。渐近方差取决于未知球半径平方分布函数$F$在估计点及零点处的局部光滑性。我们在某些局部光滑性条件下，证明了相应的局部渐近极小化极大下界。这以自适应方式解决了该非参数估计问题。