Nonparametric Estimation of Surface Integrals on Density Level Sets
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The estimation of surface integrals on density level sets is important (such as for confidence regions and bandwidth selection) in the study of nonparametric level set estimation. We consider a plug-in estimator based on kernel density estimation. By establishing a diffeomorphism between the true and estimated density level sets, we obtain the asymptotic normality of our estimator of the surface integrals when the integrand is known. We also consider the convergence rate of a plug-in bandwidth selector for density level set estimation, which involves the density derivatives as unknown integrands.
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