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arXiv · 0908.1045

Asymptotic normality of plug-in level set estimates

David M. Mason·Wolfgang Polonik
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Abstract

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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David M. Mason, Wolfgang Polonik. 2009-08-07. Asymptotic normality of plug-in level set estimates. https://doi.org/10.1214/08-aap569

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