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2020 Asymptotics and optimal bandwidth for nonparametric estimation of density level sets
Wanli Qiao
Electron. J. Statist. 14(1): 302-344 (2020). DOI: 10.1214/19-EJS1668


Bandwidth selection is crucial in the kernel estimation of density level sets. A risk based on the symmetric difference between the estimated and true level sets is usually used to measure their proximity. In this paper we provide an asymptotic $L^{p}$ approximation to this risk, where $p$ is characterized by the weight function in the risk. In particular the excess risk corresponds to an $L^{2}$ type of risk, and is adopted to derive an optimal bandwidth for nonparametric level set estimation of $d$-dimensional density functions ($d\geq 1$). A direct plug-in bandwidth selector is developed for kernel density level set estimation and its efficacy is verified in numerical studies.


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Wanli Qiao. "Asymptotics and optimal bandwidth for nonparametric estimation of density level sets." Electron. J. Statist. 14 (1) 302 - 344, 2020.


Received: 1 April 2019; Published: 2020
First available in Project Euclid: 8 January 2020

zbMATH: 1428.62184
MathSciNet: MR4048601
Digital Object Identifier: 10.1214/19-EJS1668

Primary: 62G20
Secondary: 62G05

Keywords: kernel density estimation , Level set , optimal bandwidth , symmetric difference


Vol.14 • No. 1 • 2020
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