Principe de grandes déviations uniforme pour l'estimateur de la densité par la méthode des delta-suites

In this Note, we obtain a large deviations principle for the uniform deviation of the delta-sequence density estimator. A general result is stated for any regular delta-sequence and a discussion of hypotheses for the most usual methods is given. Implications of our results in the study of the inaccuracy rate of these estimates with the comparisons of performances of various methods are given. The estimation is based upon sequences of i.i.d. random variables. To cite this article: N. Berrahou, C. R. Acad. Sci. Paris, Ser. I 343 (2006).