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

Christophe Chesneau

doi:10.1214/07-ejs067

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arXiv · 0708.4104

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

Christophe Chesneau

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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,...).

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BibTeX RIS

Christophe Chesneau. 2007-08-30. Wavelet block thresholding for samples with random design: a minimax approach under the $L^p$ risk. https://doi.org/10.1214/07-ejs067

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