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dc.contributor.authorBalabdaoui, Fadoua
dc.date.accessioned2010-01-26T15:52:58Z
dc.date.available2010-01-26T15:52:58Z
dc.date.issued2007
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/3145
dc.language.isoenen
dc.subjectConvex densityen
dc.subjectHampel's problemen
dc.subjectestimation at the boundaryen
dc.subjectBrownian motionen
dc.subject.ddc519en
dc.titleConsistent estimation of a convex density at the originen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenMotivated by Hampel's birds migration problem, \mycite{gjw:01b} established the asymptotic distribution theory for the nonparametric Least Squares and Maximum Likelihood estimators of a convex and decreasing density, $g_0$, at a fixed point $t_0 > 0$. However, estimation of the distribution function of the birds' resting times involves estimation of $g'_0$ at 0, a boundary point at which the estimators are not consistent. In this paper, we focus on the Least Squares estimator, $\tilde{g}_n$. Our goal is to show that consistent estimators of both $g_0(0)$ and $g'_0(0)$ can be based solely on $\tilde{g}_n$. Following the idea of \mycite{kuliandlopuh:06} in monotone estimation, we show that it suffices to take $\tilde{g}_n(n^{-\alpha})$ and $\tilde{g}'_n(n^{-\alpha})$, with $\alpha \in (0,1/3)$. We establish their joint asymptotic distributions and show that $\alpha =1/5$ should be taken as it yields the fastest rates of convergence.en
dc.relation.isversionofjnlnameMathematical Methods of Statistics
dc.relation.isversionofjnlvol16en
dc.relation.isversionofjnlissue2en
dc.relation.isversionofjnldate2007
dc.relation.isversionofjnlpages77-95en
dc.relation.isversionofdoihttp://dx.doi.org/10.3103/S1066530707020019en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherAllerton Press, Inc.en
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


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