A maxiset approach of a Gaussian noise model
Résumé
We consider the problem of estimating an unknown function $f$ in a Gaussian white noise setting under $\mathbb{L}^p$ risk. We investigate the minimax rate of convergence over usual Besov spaces and over weighted Besov spaces. We show via the maxiset approach that the natural hard thresholding procedure constructed on warped wavelet bases is close to the optimal over weighted Besov spaces.