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Comptes Rendus Mathématique
Volume 337, n° 1
pages 67-70 (juillet 2003)
Doi : 10.1016/S1631-073X(03)00259-0
Received : 20 February 2003 ;  accepted : 19 May 2003
Vitesse de convergence uniforme presque sûre de l'estimateur linéaire par méthode d'ondelettes
Rate of almost sure uniform convergence of the linear wavelet density estimator

Anne  Massiani
Université Paris 6, LSTA, boîte 158, 175, rue du Chevaleret, 75013 Paris, France 

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Nous établissons une loi du logarithme itéré en norme uniforme pour l'estimateur linéaire par méthode d'ondelettes. La preuve de ce résultat est basée sur une loi du logarithme itéré fonctionnelle pour les accroissements du processus empirique uniforme démontrée par Deheuvels et Mason (Ann. Probab. 20 (1992) 1248-1287). Pour citer cet article : A. Massiani, C. R. Acad. Sci. Paris, Ser. I 337 (2003).

Abstract

We establish an uniform law of the iterated logarithm for the linear wavelet density estimator. A key tool in the proof of this result is the functional law of the iterated logarithm for the increments of the empirical process proved by Deheuvels and Mason (Ann. Probab. 20 (1992) 1248-1287). To cite this article: A. Massiani, C. R. Acad. Sci. Paris, Ser. I 337 (2003).




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