标题： 关于使用树结构的新阈值化方法的性能 显示英文标题

标题： On the performances of a new thresholding procedure using tree structure

摘要： 本文研究了函数估计问题。利用白噪声模型框架，我们提供了一种基于阈值规则构造新小波方法的途径，该方法利用了小波分解的二进制结构。我们证明，这种新方法表现非常出色：一方面，它在一大类 Besov 空间上具有自适应性和接近极小-极大性；另一方面，该方法达到给定收敛速度的最大函数空间（maxiset）非常大。不仅如此，通过研究其 maxiset 的形状，我们证明了新方法优于硬阈值方法。 显示英文摘要

摘要： This paper deals with the problem of function estimation. Using the white noise model setting, we provide a method to construct a new wavelet procedure based on thresholding rules which takes advantage of the dyadic structure of the wavelet decomposition. We prove that this new procedure performs very well since, on the one hand, it is adaptive and near-minimax over a large class of Besov spaces and, on the other hand, the maximal functional space (maxiset) where this procedure attains a given rate of convergence is very large. More than this, by studying the shape of its maxiset, we prove that the new procedure outperforms the hard thresholding procedure.