Adapting to Unknown Smoothness by Aggregation of Thresholded Wavelet Estimators

Details Adapting to Unknown Smoothness by Aggregation of Thresholded Wavelet Estimators Adapting to Unknown Smoothness by Aggregation of Thresholded Wavelet Estimators

2006-12-19

arxiv.org/abs/math/0612546v1

Mathematics

Statistics Theory

Scientific paper

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.

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