Towards a universally consistent estimator of the Minkowski content
We deal with a subject in the interplay between nonparametric statistics and geometric measure theory. The measure () of the boundary of a set ⊂ ℝ (with ≥ 2) can be formally defined, a simple limit, by the so-called Minkowski content. We study the estimation of () from a sample of random points inside and outside . The sample design assumes that, for each sample point, we know (without error) whether or not that point belongs to . Under this design we suggest a...