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Title: Hyperbolic wavelet thresholding methods and the curse of dimensionality through the maxiset approach
Authors: Autin, F.
Claeskens, Gerda
Freyermuth, Jean-Marc
Issue Date: Sep-2012
Publisher: KU Leuven - Faculty of Economics and Business
Series Title: FEB Research Report KBI_1219 pages:1-25
Abstract: In this paper we compute the maxisets of some denoising methods (estimators) for multidimensional signals based on thresholding coefficients in hyperbolic wavelet bases. That is, we determine the largest functional space over which the risk of these estimators converges at a chosen rate. In the unidimensional setting, refining the choice of the coefficients that are subject to thresholding by pooling information from geometric structures in the coefficient
domain (e.g., vertical blocks) is known to provide 'large maxisets'. In the multidimensional setting, the situation is less straightforward. In a sense these estimators are much more exposed to the curse of dimensionality. However we identify cases where information pooling has a clear benefit. In particular, we identify some general structural constraints that can be related to compound models and to a `minimal' level of anisotropy.
Publication status: published
KU Leuven publication type: IR
Appears in Collections:Research Center for Operations Research and Business Statistics (ORSTAT), Leuven

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