Wavelet block thresholding for samples with random design: a minimax approach under the $L^p$ risk

Abstract

We consider the regression model with (known) random design. We investigate the minimax performances of an adaptive wavelet block thresholding estimator under the ${\mathbb{L}}^p$ risk with $p\ge 2$ over Besov balls. We prove that it is near optimal and that it achieves better rates of convergence than the conventional term-by-term estimators (hard, soft,...).

Published at http://dx.doi.org/10.1214/07-EJS067 in the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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