Electronic Journal of Statistics
- Electron. J. Statist.
- Volume 13, Number 1 (2019), 985-1030.
Nonparametric confidence regions for level sets: Statistical properties and geometry
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.
Electron. J. Statist., Volume 13, Number 1 (2019), 985-1030.
Received: July 2018
First available in Project Euclid: 30 March 2019
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Qiao, Wanli; Polonik, Wolfgang. Nonparametric confidence regions for level sets: Statistical properties and geometry. Electron. J. Statist. 13 (2019), no. 1, 985--1030. doi:10.1214/19-EJS1543. https://projecteuclid.org/euclid.ejs/1553911237