Abstract:The kernel method of estimation of curves is now popular and widely used in statistical applications. Kernel estimators suffer from boundary effects, however, when the support of the function to be estimated has finite endpoints. Several solutions to this problem have already been proposed. Here the authors develop a new method of boundary correction for kernel density estimation. Their technique is a kind of generalized reflection involving transformed data. It generates a class of boundary corrected estimators having desirable properties such as local smoothness and nonnegativity. Simulations show that the proposed method performs quite well when compared with the existing methods for almost all shapes of densities. The authors present the theory behind this new methodology, and they determine the bias and variance of their estimators.Une methode de reflexion generalisee pour la correction des effets de frontiere en estimation par noyau Rhunk' : L'estimation de courbes par la mkthode du noyau est dorknavant populaire et largement utiliske en statistique appliqube. Les estimateurs B noyau sont toutefois sujets A des effets de bord, lorsque le support de la fonction h estimer est fiN. Quelques solutions B ce probltme ont dkjA 6tk propostes. Les auteurs dkveloppent ici une nouvelle mtthode de correction des estimations A noyau de densitk. Leur technique fait intervenir une sorte de rbflexion gbntralis& de donnQs transformbes. Elle gbntre une classe d'estimateurs comgts pour les bords posskdant de bonnes propriktks, dont une rkgularitk locale et la non-nkgativitk. Des simulations montrent que la mkthode proposbe se comporte bien par rapport aux techniques existantes, et ce pour presque toutes les formes de densitks. Les auteurs prksentent la thborie sous-jacente A cette nouvelle mtthodologie et ils dtterminent le biais et la variance de leurs estimateurs.
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