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Asymptotics and Optimal Bandwidth for Nonparametric Estimation of Density Level Sets (1707.09697v3)

Published 31 Jul 2017 in math.ST and stat.TH

Abstract: 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 $Lp$ approximation to this risk, where $p$ is characterized by the weight function in the risk. In particular the excess risk corresponds to an $L2$ 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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