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2009 Asymptotic Normality in Density Support Estimation
Gérard Biau, Benoit Cadre, David Mason, Bruno Pelletier
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Electron. J. Probab. 14: 2617-2635 (2009). DOI: 10.1214/EJP.v14-722


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.


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Gérard Biau. Benoit Cadre. David Mason. Bruno Pelletier. "Asymptotic Normality in Density Support Estimation." Electron. J. Probab. 14 2617 - 2635, 2009.


Accepted: 9 December 2009; Published: 2009
First available in Project Euclid: 1 June 2016

zbMATH: 1185.62071
MathSciNet: MR2570013
Digital Object Identifier: 10.1214/EJP.v14-722

Primary: 62G05
Secondary: 62G20

Keywords: central limit theorem , nonparametric statistics , support estimation , Tubular neighborhood

Vol.14 • 2009
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