On the performances of a new thresholding procedure using tree structure
Florent Autin
Source: Electron. J. Statist. Volume 2
(2008), 412-431.
Abstract
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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Keywords: Besov spaces; estimation; maxiset; minimax risk; rate of convergence; thresholding methods; tree structure
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.ejs/1211512580
Digital Object Identifier: doi:10.1214/08-EJS205
Mathematical Reviews number (MathSciNet): MR2411441
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