Minimax Hausdorff estimation of density level sets
Statistics Theory
2019-05-09 v1 Methodology
Statistics Theory
Abstract
Given a random sample of points from some unknown density, we propose a data-driven method for estimating density level sets under the r-convexity assumption. This shape condition generalizes the convexity property. However, the main problem in practice is that r is an unknown geometric characteristic of the set related to its curvature. A stochastic algorithm is proposed for selecting its optimal value from the data. The resulting reconstruction of the level set is able to achieve minimax rates for Hausdorff metric and distance in measure, up to log factors, uniformly on the level of the set.
Cite
@article{arxiv.1905.02897,
title = {Minimax Hausdorff estimation of density level sets},
author = {Alberto Rodríguez-Casal and Paula Saavedra-Nieves},
journal= {arXiv preprint arXiv:1905.02897},
year = {2019}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1411.7687