Resumen de Thresholding algorithms, maxisets and well-concentrated bases

Gérard Kerkyacharian, Dominique Picard

• The aim of this paper la to synthetically analyse the performances of thresholding and wavelet estimation methods. In this connection, it la useful to describe the maxlmal sets where these methods attain a special rate of convergence. We relate these "maxisets" to other problems naturally arising in the context of non parametnc estimation, as approximation theory or information reduction. A second part of the paper is devoted to isolate two very special properties especially shared by wavelet bases, which allow them to behave almost as in an Hilbertian context even for L, risks