Asymptotic normality of plug-in level set estimates

Details Asymptotic normality of plug-in level set estimates Asymptotic normality of plug-in level set estimates

2009-08-07

arxiv.org/abs/0908.1045v1

Annals of Applied Probability 2009, Vol. 19, No. 3, 1108-1142

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/08-AAP569 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/08-AAP569

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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