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Asymptotic normality of plug-in level set estimates. (English) Zbl 1180.62048
Summary: 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.

MSC:
62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference
60F05 Central limit and other weak theorems
62E20 Asymptotic distribution theory in statistics
60F15 Strong limit theorems
Software:
Valmet
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