Asymptotic normality of plug-in level set estimates
Probability
2009-08-10 v1
Abstract
We establish the asymptotic normality of the -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.
Keywords
Cite
@article{arxiv.0908.1045,
title = {Asymptotic normality of plug-in level set estimates},
author = {David M. Mason and Wolfgang Polonik},
journal= {arXiv preprint arXiv:0908.1045},
year = {2009}
}
Comments
Published in at http://dx.doi.org/10.1214/08-AAP569 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)