TEST

, Volume 16, Issue 3, pp 523–546 | Cite as

A maxiset approach of a Gaussian noise model

Original Paper
First Online:
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Abstract

We consider the problem of estimating an unknown function f in a Gaussian noise setting under the global \(\mathbb{L}^{p}\) risk. The particularity of the model considered is that it utilizes a secondary function v which complicates the estimate significantly. While varying the assumptions on this function, we investigate the minimax rate of convergence over two types of Besov balls. One is defined as usual and the other belongs to the family of weighted spaces. Adopting the maxiset approach, we show that a natural hard thresholding procedure attained the minimax rate of convergence within a logarithmic factor over such weighted Besov balls.

Keywords

Gaussian noise Warped wavelets Besov spaces Minimax Muckenhoupt weights Wavelet thresholding Maxiset 

Mathematics Subject Classification (2000)

62G07 62G20 42B20 
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Copyright information

© Sociedad de Estadística e Investigación Operativa 2007

Authors and Affiliations

  1. 1.Laboratoire de Probabilités et Modèles Aléatoires, CNRS-UMR 7599Université Paris VI, UFR de MathématiquesParisFrance

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