ASYMPTOTIC NORMALITY OF PLUG-IN LEVEL SET ESTIMATES

• 成果类型: Article
• 署名作者: Mason, David M.; Polonik, Wolfgang
• 署名单位: University of Delaware; University of California System; University of California Davis
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/08-AAP569
• 发表日期: 2009
• 页码: 1108-1142
• 关键词: nonparametric-estimation; DENSITY-ESTIMATION; convergence-rates; Novelty Detection; Visualization; Consistency; contour

摘要

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.