Nonparametric Confidence Regions for Level Sets: Statistical Properties and Geometry
Statistics Theory
2019-03-05 v1 Statistics Theory
Abstract
This paper studies and critically discusses the construction of nonparametric confidence regions for density level sets. Methodologies based on both vertical variation and horizontal variation are considered. The investigations provide theoretical insight into the behavior of these confidence regions via large sample theory. We also discuss the geometric relationships underlying the construction of horizontal and vertical methods, and how finite sample performance of these confidence regions is influenced by geometric or topological aspects. These discussions are supported by numerical studies.
Cite
@article{arxiv.1903.01430,
title = {Nonparametric Confidence Regions for Level Sets: Statistical Properties and Geometry},
author = {Wanli Qiao and Wolfgang Polonik},
journal= {arXiv preprint arXiv:1903.01430},
year = {2019}
}
Comments
46 pages, 2 figures