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Maxisets for linear procedures

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  • Rivoirard, Vincent

Abstract

We study maxisets for linear procedures in the framework of the heteroscedastic white noise model. This enables us to point out the nature of the spaces naturally connected to these procedures and to compare the performance of linear and nonlinear estimates by comparing their respective maxisets.

Suggested Citation

  • Rivoirard, Vincent, 2004. "Maxisets for linear procedures," Statistics & Probability Letters, Elsevier, vol. 67(3), pages 267-275, April.
    • Handle: RePEc:eee:stapro:v:67:y:2004:i:3:p:267-275
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    References listed on IDEAS

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    1. Gérard Kerkyacharian & Dominique Picard & Lucien Birgé & Peter Hall & Oleg Lepski & Enno Mammen & Alexandre Tsybakov & G. Kerkyacharian & D. Picard, 2000. "Thresholding algorithms, maxisets and well-concentrated bases," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(2), pages 283-344, December.
    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.
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    Cited by:

    1. Chesneau, Christophe, 2008. "On the maxiset comparison between hard and block thresholding methods," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 675-681, April.
    2. Peng, Jingfu, 2023. "Adaptive and efficient estimation in the Gaussian sequence model," Statistics & Probability Letters, Elsevier, vol. 195(C).
    3. Karine Bertin & Vincent Rivoirard, 2009. "Maxiset in sup-norm for kernel estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(3), pages 475-496, November.

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