文章基本信息

标题：Bandwidth selection for kernel density estimators of multivariate level sets and highest density regions
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作者：Charles R. Doss ; Guangwei Weng
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2018
卷号：12
期号：2
页码：4313-4376
DOI：10.1214/18-EJS1501
语种：English
出版社：Institute of Mathematical Statistics
摘要：We consider bandwidth matrix selection for kernel density estimators of density level sets in $\mathbb{R} ^{d}$, $d\ge 2$. We also consider estimation of highest density regions, which differs from estimating level sets in that one specifies the probability content of the set rather than specifying the level directly. This complicates the problem. Bandwidth selection for KDEs is well studied, but the goal of most methods is to minimize a global loss function for the density or its derivatives. The loss we consider here is instead the measure of the symmetric difference of the true set and estimated set. We derive an asymptotic approximation to the corresponding risk. The approximation depends on unknown quantities which can be estimated, and the approximation can then be minimized to yield a choice of bandwidth, which we show in simulations performs well. We provide an R package lsbs for implementing our procedure.