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On the maxiset comparison between hard and block thresholding methods

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  • Chesneau, Christophe

Abstract

Autin [2007. Maxisets for [mu]-thresholding rules. Test, to appear, see ] has established the following estimation result: by considering the Gaussian white noise model and the Besov risk , the BlockShrink estimator is better in the maxiset sense than the hard thresholding estimator. In the present paper, we show that this maxiset superiority is strict and can be extended to the risk for numerous sophisticated models (regression with random uniform design, convolution model in Gaussian white noise,...).

Suggested Citation

  • Chesneau, Christophe, 2008. "On the maxiset comparison between hard and block thresholding methods," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 675-681, April.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:6:p:675-681
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    References listed on IDEAS

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    1. Rivoirard, Vincent, 2004. "Maxisets for linear procedures," Statistics & Probability Letters, Elsevier, vol. 67(3), pages 267-275, April.
    2. 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.
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    Cited by:

    1. Florent Autin & Jean-Marc Freyermuth & Rainer Von Sachs, 2014. "Block-threshold-adapted Estimators via a Maxiset Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(1), pages 240-258, March.

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