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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