Asymptotics and Optimal Bandwidth for Nonparametric Estimation of Density Level Sets

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 $L^p$ 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 ($d\ge 1$). A direct plug-in bandwidth selector is developed for kernel density level set estimation and its efficacy is verified in numerical studies.

43 pages, 4 figures

References in corpus (5)

• Choice of neighbor order in nearest-neighbor classification
• Asymptotic normality of plug-in level set estimates
• Asymptotics and optimal bandwidth selection for highest density region estimation
• Nonparametric estimation of surface integrals
• Confidence regions for excursion sets in asymptotically Gaussian random fields, with an application to climate

Cited by in corpus (1)

• Nonparametric Inference via Bootstrapping the Debiased Estimator