On the performances of a new thresholding procedure using tree structure

Details On the performances of a new thresholding procedure using tree structure On the performances of a new thresholding procedure using tree structure

2008-03-12

arxiv.org/abs/0803.1753v2

Electronic Journal of Statistics 2008, Vol. 2, 412-431

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/08-EJS205 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by t

Scientific paper

10.1214/08-EJS205

This paper deals with the problem of function estimation. Using the white noise model setting, we provide a method to construct a new wavelet procedure based on thresholding rules which takes advantage of the dyadic structure of the wavelet decomposition. We prove that this new procedure performs very well since, on the one hand, it is adaptive and near-minimax over a large class of Besov spaces and, on the other hand, the maximal functional space (maxiset) where this procedure attains a given rate of convergence is very large. More than this, by studying the shape of its maxiset, we prove that the new procedure outperforms the hard thresholding procedure.

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