| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 9519888 | Comptes Rendus Mathematique | 2005 | 4 Pages |
Abstract
We study the problem of the nonparametric estimation of a probability density in L2(R). Expressing the mean integrated squared error in the Fourier domain, we show that it is close to the mean squared error in the Gaussian sequence model. Then, applying a modified version of Stein's blockwise method, we obtain a linear monotone oracle inequality and a kernel oracle inequality. As a consequence, the proposed estimator is sharp minimax adaptive (i.e. up to a constant) on a scale of Sobolev classes of densities. To cite this article: Ph. Rigollet, C. R. Acad. Sci. Paris, Ser. I 340 (2005).
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Philippe Rigollet,