Asymptotics and optimal bandwidth for nonparametric estimation of density level sets

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 >= 1). A direct plug-in bandwidth selector is developed for kernel density level set estimation and its efficacy is verified in numerical studies.