David M. Mason, Wolfgang Polonik
Published 2009-08-07Version 1
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.
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)
Journal: Annals of Applied Probability 2009, Vol. 19, No. 3, 1108-1142
Estimates of the rate of approximation in the CLT for $L_1$-norm of density estimators
Weighted uniform consistency of kernel density estimators
Asymptotic normality and greatest common divisors
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