Asymptotic confidence bands for the histogram regression estimator
Statistics Theory
2026-03-02 v2 Methodology
Statistics Theory
Abstract
Asymptotic uniform confidence bands are constructed for a multivariate nonparametric regression model with heteroscedastic noise, employing histogram estimators under flexible partition conditions. The construction is especially applicable to unsmooth regression functions of H\"older regularity less than one. While the radius of the confidence bands could be approximated via the Gumbel distribution, our construction does not depend on an extreme value distribution, but instead can be explicitly calculated for the chosen partition.
Keywords
Cite
@article{arxiv.2508.12391,
title = {Asymptotic confidence bands for the histogram regression estimator},
author = {Natalie Neumeyer and Jan Rabe and Mathias Trabs},
journal= {arXiv preprint arXiv:2508.12391},
year = {2026}
}