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Thresholding algorithms, maxisets and well-concentrated bases

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Author Info

  • Gérard Kerkyacharian
  • Dominique Picard

    ()

  • Lucien Birgé
  • Peter Hall
  • Oleg Lepski
  • Enno Mammen
  • Alexandre Tsybakov
  • G. Kerkyacharian
  • D. Picard

Abstract

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File URL: http://hdl.handle.net/10.1007/BF02595738
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Bibliographic Info

Article provided by Springer in its journal Test.

Volume (Year): 9 (2000)
Issue (Month): 2 (December)
Pages: 283-344

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Handle: RePEc:spr:testjl:v:9:y:2000:i:2:p:283-344

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Related research

Keywords: Approximation methods; Besov spaces; denoising; minimax rate of convergence; non parametric estimation; oracle inequalities; saturation spaces; wavelet thresholding; 62G05; 62G07; 62G20;

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References

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  1. Hoffmann, Marc, 1999. "On nonparametric estimation in nonlinear AR(1)-models," Statistics & Probability Letters, Elsevier, vol. 44(1), pages 29-45, August.
  2. Kerkyacharian, Gérard & Picard, Dominique, 1993. "Density estimation by kernel and wavelets methods: Optimality of Besov spaces," Statistics & Probability Letters, Elsevier, vol. 18(4), pages 327-336, November.
  3. Kerkyacharian, G. & Picard, D., 1992. "Density estimation in Besov spaces," Statistics & Probability Letters, Elsevier, vol. 13(1), pages 15-24, January.
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Citations

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Cited by:
  1. Chesneau, Christophe, 2007. "Regression with random design: A minimax study," Statistics & Probability Letters, Elsevier, vol. 77(1), pages 40-53, January.
  2. Durastanti, Claudio & Geller, Daryl & Marinucci, Domenico, 2012. "Adaptive nonparametric regression on spin fiber bundles," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 16-38, February.
  3. Rivoirard, Vincent, 2004. "Maxisets for linear procedures," Statistics & Probability Letters, Elsevier, vol. 67(3), pages 267-275, April.
  4. Chesneau, Christophe, 2008. "On the maxiset comparison between hard and block thresholding methods," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 675-681, April.
  5. Aminghafari, Mina & Cheze, Nathalie & Poggi, Jean-Michel, 2006. "Multivariate denoising using wavelets and principal component analysis," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2381-2398, May.

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