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.
Publié le : 2009-06-15
Classification:
Central limit theorem,
kernel density estimator,
level set estimation,
60F05,
60F15,
62E20,
62G07
@article{1245071021,
author = {Mason, David M. and Polonik, Wolfgang},
title = {Asymptotic normality of plug-in level set estimates},
journal = {Ann. Appl. Probab.},
volume = {19},
number = {1},
year = {2009},
pages = { 1108-1142},
language = {en},
url = {http://dml.mathdoc.fr/item/1245071021}
}
Mason, David M.; Polonik, Wolfgang. Asymptotic normality of plug-in level set estimates. Ann. Appl. Probab., Tome 19 (2009) no. 1, pp. 1108-1142. http://gdmltest.u-ga.fr/item/1245071021/