# Nonparametric Confidence Regions for Level Sets: Statistical Properties and Geometry

## TL;DR

This paper explores the theoretical properties and geometric aspects of constructing nonparametric confidence regions for density level sets, supported by numerical studies.

## Contribution

It provides a comprehensive analysis of both vertical and horizontal variation methods for confidence regions, including their geometric relationships and finite sample performance.

## Key findings

- Theoretical insights into the behavior of confidence regions via large sample theory
- Analysis of geometric and topological influences on finite sample performance
- Numerical studies validating the theoretical and geometric discussions

## 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.