Étude asymptotique locale de l'estimateur par ondelettesA law of the iterated logarithm for wavelet density estimator

We state a pointwise central limit theorem for the linear wavelet density estimator in a more general setting than the result of Wu [12]. Furthermore, we also give a pointwise law of the iterated logarithm for this density estimator. Our proof of the law of the iterated logarithm uses the results of Mason [9] on the asymptotic behavior of the tail empirical process. To cite this article: A. Massiani, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 553–556.