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Asymptotic Normality in Density Support Estimation

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Asymptotic Normality in Density Support Estimation
2.	Creator	Author's name, affiliation, country	Gérard Biau; Université Pierre et Marie Curie -- Paris VI; France
2.	Creator	Author's name, affiliation, country	Benoit Cadre; ÉNS Cachan Bretagne; France
2.	Creator	Author's name, affiliation, country	David M Mason; University of Delaware; United States
2.	Creator	Author's name, affiliation, country	Bruno Pelletier; Université Rennes 2; France
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Support estimation; Nonparametric statistics; Central limit theorem; Tubular neighborhood
3.	Subject	Subject classification	62G05; 62G20
4.	Description	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.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2009-12-09
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/722
10.	Identifier	Digital Object Identifier	10.1214/EJP.v14-722
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 14
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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