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Asymptotic Normality in Density Support Estimation

   
@article{EJP722,
	author = {Gérard Biau and Benoit Cadre and David Mason and Bruno Pelletier},
	title = {Asymptotic Normality in Density Support Estimation},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {14},
	year = {2009},
	keywords = {Support estimation; Nonparametric statistics; Central limit theorem; Tubular neighborhood},
	abstract = {Let $X_1,\ldots,X_n$ be $n$ independent observations drawn from a multivariate probability density $f$ with compact support $S_f$. This paper is devoted to the study of the estimator $\hat{S}_n$ of $S_f$ defined as the union of balls centered at the $X_i$ and with common radius $r_n$. Using tools from Riemannian geometry, and under mild assumptions on $f$ and the sequence $(r_n)$, we prove a central limit theorem for $\lambda (S_n \Delta S_f)$, where $\lambda$ denotes the Lebesgue measure on $\mathbb{R}^d$ and $\Delta$ the symmetric difference operation.},
	pages = {no. 91, 2617-2635},
	issn = {1083-6489},
	doi = {10.1214/EJP.v14-722},    
        url = {http://ejp.ejpecp.org/article/view/722}}