Estimation de la densité de probabilité améliorée par pre-testing

We consider the nonparametric problem of multidimensional probability density estimate. Using concept of minimax risk with random normalizing factor introduced by Lepski [Math. Methods Statist. 8 (1999) 441-486], by considering an independence hypothesis, we build an estimator which can be adaptive and whose accuracy, depending on the observation, is better than the minimax estimate, n−β2β+d, with prescribed confidence level. To cite this article: A.F. Yode, C. R. Acad. Sci. Paris, Ser. I 340 (2005).