Consistency of the beta kernel density function estimator

The authors give the exact asymptotic behaviour of the expected average absolute error of a beta kernel density estimator proposed by Chen (1999). They also prove the uniform weak consistency of this estimator for the class of continuous densities. /// Les auteurs donnent le comportement asymptotiqu...

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Veröffentlicht in:	Canadian journal of statistics 2003-03, Vol.31 (1), p.89-98
Hauptverfasser:	Bouezmarni, Taoufik, Rolin, Jean-Marie
Format:	Artikel
Sprache:	eng
Schlagworte:	Asymptotic behaviour asymptotics beta kernel Consistent estimators Convergence Density Density distributions Density estimation Error Estimation Estimation bias Estimators L1 error Mathematical independent variables Mathematics Random variables Statistical methods Statistics weak convergence
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Zusammenfassung:	The authors give the exact asymptotic behaviour of the expected average absolute error of a beta kernel density estimator proposed by Chen (1999). They also prove the uniform weak consistency of this estimator for the class of continuous densities. /// Les auteurs donnent le comportement asymptotique exact de l'espérance de l'erreur en valeur absolue pour un estimateur de densité par noyau bêta proposé par Chen (1999). Ils en démontrent la convergence faible uniforme pour la classe des densités continues.
ISSN:	0319-5724 1708-945X
DOI:	10.2307/3315905