A note on kernel density estimators with optimal bandwidths
Statistics Theory
2026-04-17 v1 Statistics Theory
Abstract
We show that the cumulative distribution function corresponding to a kernel density estimator with optimal bandwidth lies outside any confidence interval, around the empirical distribution function, with probability tending to 1 as the sample size increases.
Cite
@article{arxiv.2604.14181,
title = {A note on kernel density estimators with optimal bandwidths},
author = {Nils Lid Hjort and Stephen G. Walker},
journal= {arXiv preprint arXiv:2604.14181},
year = {2026}
}
Comments
8 pages, 0 figures. Statistical Research Report, Department of Mathematics, University of Oslo, from June 2000, but arXiv'd April 2026. The papers is pubished in essentially this form in Statistics & Probabiity Letters, 2001, vol. 54, pages 153-159, at this url: https://www.sciencedirect.com/science/article/pii/S016771520100027X