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June 2009 Asymptotic normality of plug-in level set estimates
David M. Mason, Wolfgang Polonik
Ann. Appl. Probab. 19(3): 1108-1142 (June 2009). DOI: 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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David M. Mason. Wolfgang Polonik. "Asymptotic normality of plug-in level set estimates." Ann. Appl. Probab. 19 (3) 1108 - 1142, June 2009.


Published: June 2009
First available in Project Euclid: 15 June 2009

zbMATH: 1180.62048
MathSciNet: MR2537201
Digital Object Identifier: 10.1214/08-AAP569

Primary: 60F05 , 60F15 , 62E20 , 62G07

Keywords: central limit theorem , kernel density estimator , level set estimation

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.19 • No. 3 • June 2009
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