A maxiset approach of a Gaussian noise model

摘要

We consider the problem of estimating an unknown function f in a Gaussian noise setting under the global $mathbb{L}^{p}$ risk. The particularity of the model considered is that it utilizes a secondary function v which complicates the estimate significantly. While varying the assumptions on this function, we investigate the minimax rate of convergence over two types of Besov balls. One is defined as usual and the other belongs to the family of weighted spaces. Adopting the maxiset approach, we show that a natural hard thresholding procedure attained the minimax rate of convergence within a logarithmic factor over such weighted Besov balls.