IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v67y2004i3p267-275.html
   My bibliography  Save this article

Maxisets for linear procedures

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(04)00038-0
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Peng, Jingfu, 2023. "Adaptive and efficient estimation in the Gaussian sequence model," Statistics & Probability Letters, Elsevier, vol. 195(C).
    2. 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.
    3. Chesneau, Christophe, 2008. "On the maxiset comparison between hard and block thresholding methods," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 675-681, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Durastanti, Claudio, 2016. "Adaptive global thresholding on the sphere," Journal of Multivariate Analysis, Elsevier, vol. 151(C), pages 110-132.
    2. Kato, Takeshi, 1999. "Density estimation by truncated wavelet expansion," Statistics & Probability Letters, Elsevier, vol. 43(2), pages 159-168, June.
    3. Gaëlle Chagny & Claire Lacour, 2015. "Optimal adaptive estimation of the relative density," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 605-631, September.
    4. Hohage, Thorsten & Maréchal, Pierre & Simar, Léopold & Vanhems, Anne, 2024. "A Mollifier Approach To The Deconvolution Of Probability Densities," Econometric Theory, Cambridge University Press, vol. 40(2), pages 320-359, April.
    5. Gérard, Kerkyacharian & Dominique, Picard, 1997. "Limit of the quadratic risk in density estimation using linear methods," Statistics & Probability Letters, Elsevier, vol. 31(4), pages 299-312, February.
    6. Hoffmann, Marc, 1999. "Adaptive estimation in diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 79(1), pages 135-163, January.
    7. Ammous, Sinda & Dedecker, Jérôme & Duval, Céline, 2024. "Adaptive directional estimator of the density in Rd for independent and mixing sequences," Journal of Multivariate Analysis, Elsevier, vol. 203(C).
    8. Koo, Ja-Yong & Kim, Woo-Chul, 1996. "Wavelet density estimation by approximation of log-densities," Statistics & Probability Letters, Elsevier, vol. 26(3), pages 271-278, February.
    9. Autin, Florent & Freyermuth, Jean-Marc & von Sachs, Rainer, 2011. "Combining thresholding rules: a new way to improve the performance of wavelet estimators," LIDAM Discussion Papers ISBA 2011021, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. Chesneau, Christophe, 2007. "Regression with random design: A minimax study," Statistics & Probability Letters, Elsevier, vol. 77(1), pages 40-53, January.
    11. 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.
    12. Chesneau, Christophe, 2008. "On the maxiset comparison between hard and block thresholding methods," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 675-681, April.
    13. Peng, Jingfu, 2023. "Adaptive and efficient estimation in the Gaussian sequence model," Statistics & Probability Letters, Elsevier, vol. 195(C).
    14. 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.
    15. F. Autin & J.-M. Freyermuth & R. von Sachs, 2012. "Combining thresholding rules: a new way to improve the performance of wavelet estimators," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(4), pages 905-922, December.
    16. Liang Han-Ying & Mammitzsch Volker & Steinebach Josef, 2005. "Nonlinear wavelet density and hazard rate estimation for censored data under dependent observations," Statistics & Risk Modeling, De Gruyter, vol. 23(3), pages 161-180, March.
    17. Aya-Moreno, Carlos & Geenens, Gery & Penev, Spiridon, 2018. "Shape-preserving wavelet-based multivariate density estimation," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 30-47.
    18. 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.
    19. Marina Vannucci & Brani Vidakovic, 1997. "Preventing the Dirac disaster: Wavelet based density estimation," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 6(2), pages 145-159, August.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:67:y:2004:i:3:p:267-275. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.