Asymptotic normality of plug-in level set estimates
Authors:
- David M. MasonDMDavid M. Mason
- Wolfgang PolonikWPWolfgang Polonik
Open Access
- 1 June 2009
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Applied Probability
- Vol. 19 (3) , 1108-1142
Abstract
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.Keywords
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