Adapting to Unknown Smoothness by Aggregation of Thresholded Wavelet Estimators

By Christophe Chesneau, Guillaume Lecué. 2006

10 citations recorded by the source corpus.

We study the performances of an adaptive procedure based on a convex combination, with data-driven weights, of term-by-term thresholded wavelet estimators. For the bounded regression model, with random uniform design, and the nonparametric density model, we show that the resulting estimator is optimal in the minimax sense over all Besov balls under the $L^2$ risk, without any logarithm factor.

Subfields: Statistics and Probability

Citations in the corpus

• Smoothness, Low Noise and Fast Rates (2010, neutral): “Chesneau et al [10] extend Tsybakov’s work also to general losses, deriving similar results for Lipschitz loss function.”