Title: Asymptotics and Optimal Bandwidth Selection for Nonparametric Estimation of Density Level Sets,
Abstract: Bandwidth selection is crucial in the kernel estimation of density level
sets. 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 in an optimal bandwidth selection rule
for nonparametric level set estimation of $d$-dimensional density functions
($d\geq 1$).