Abstract: We consider a multi-wavelet thresholding method for nonparametric estimation. An adaptive procedure based on a convex combination of weighted term-by-term thresholded wavelet estimators is proposed. By considering the density estimation framework, we prove that this procedure is optimal in the minimax sense over Besov balls under therisk, without an extra logarithm term.
Key words and phrases: Aggregation, density estimation, margin, oracle inequalities, threshold estimators, wavelets.