Shape Constraint Inference

We consider the nonparametric estimation in the so-called Wicksell’s problem and we show that the isotonized version of the plug-in …

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.

We implemented in Python the Isotonic estimator of the paper “Efficient Isotonic Estimation in Wicksell Problem”. We created a dedicated library that can be installed by any Python user willing to deploy this estimator. In the library is contained also a tester where the user can test the estimator choosing from a set of hidden distribution functions F of the radii distribution.