A maxiset approach of a Gaussian noise model

• Autores: Christophe Chesneau
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 16, Nº. 3, 2007, págs. 523-546
• Idioma: inglés
• DOI: 10.1007/s11749-006-0018-6
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• Resumen

  • We consider the problem of estimating an unknown function f in a Gaussian noise setting under the global Lp 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.