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Article Dans Une Revue Electronic Journal of Probability Année : 2009

Asymptotic Normality in Density Support Estimation

Résumé

Let $X_1,\dots,X_n$ 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 unions of balls centered at the $X_i$ and of 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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Dates et versions

hal-00380359 , version 1 (30-04-2009)

Identifiants

Citer

Gérard Biau, Benoît Cadre, David Y. Mason, Bruno Pelletier. Asymptotic Normality in Density Support Estimation. Electronic Journal of Probability, 2009, 14 (91), pp.2617-2635. ⟨10.1214/EJP.v14-722⟩. ⟨hal-00380359⟩
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