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

Christophe Chesneau

doi:10.1214/07-EJS067

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

Statistics Theory 2011-11-10 v1 Statistics Theory

Authors: 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,...).

Keywords

statistical estimation maximum likelihood estimation density estimation

Cite

@article{arxiv.0708.4104,
  title  = {Wavelet block thresholding for samples with random design: a minimax approach under the $L^p$ risk},
  author = {Christophe Chesneau},
  journal= {arXiv preprint arXiv:0708.4104},
  year   = {2011}
}

Comments

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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