# Asymptotic normality of plug-in level set estimates.

@article{Mason2008AsymptoticNO, title={Asymptotic normality of plug-in level set estimates.}, author={David M. Mason and Wolfgang Polonik}, journal={Annals of Applied Probability}, year={2008}, volume={19}, pages={1108-1142} }

We establish the asymptotic normality of the $G$-measure of the symmetric difference between the level set and a plug-in-type estimator of it formed by replacing the density in the definition of the level set by a kernel density estimator. Our proof will highlight the efficacy of Poissonization methods in the treatment of large sample theory problems of this kind.

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