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

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

2007-08-30

arxiv.org/abs/0708.4104v1

Electronic Journal of Statistics 2007, Vol. 1, 331-346

Mathematics

Statistics Theory

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

Scientific paper

10.1214/07-EJS067

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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