IDEAS home Printed from https://ideas.repec.org/a/taf/gnstxx/v24y2012i4p905-922.html
   My bibliography  Save this article

Combining thresholding rules: a new way to improve the performance of wavelet estimators

Author

Listed:
  • F. Autin
  • J.-M. Freyermuth
  • R. von Sachs

Abstract

In this paper, we address the situation where we cannot differentiate wavelet-based threshold procedures because their sets of well-estimated functions (maxisets) are not nested. As a generic solution, we propose to proceed via a combination of these procedures in order to achieve new procedures which perform better in the sense that the involved maxisets contain the union of the previous ones. Throughout the paper we propose illuminating interpretations of the maxiset results and provide conditions to ensure that this combination generates larger maxisets. As an example, we propose to combine vertical- and horizontal-block thresholding procedures that are already known to perform well. We discuss the limitation of our method, and we check our theoretical results through numerical experiments.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:gnstxx:v:24:y:2012:i:4:p:905-922
    DOI: 10.1080/10485252.2012.709854
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/10485252.2012.709854
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/10485252.2012.709854?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Autin, F. & Freyermuth, Jean-Marc & von Sachs, Rainer, 2011. "Ideal denoising within a family of tree-structured wavelet estimators," LIDAM Discussion Papers ISBA 2011002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Engel, J., 1994. "A Simple Wavelet Approach to Nonparametric Regression from Recursive Partitioning Schemes," Journal of Multivariate Analysis, Elsevier, vol. 49(2), pages 242-254, May.
    4. Cai, T. Tony, 2008. "On information pooling, adaptability and superefficiency in nonparametric function estimation," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 421-436, March.
    5. Autin, Florent & Freyermuth, Jean-Marc & von Sachs, Rainer, 2011. "Ideal denoising within a family of tree-structured wavelet estimators," LIDAM Reprints ISBA 2011037, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Stuart Barber & Guy P. Nason, 2004. "Real nonparametric regression using complex wavelets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(4), pages 927-939, 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. 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.

    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. 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).
    2. Autin, Florent & Freyermuth, Jean-Marc & von Sachs, Rainer, 2011. "Block-Threshold-Adapted Estimators via a maxiset approach," LIDAM Discussion Papers ISBA 2011017, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Reményi, Norbert & Vidakovic, Brani, 2013. "Λ-neighborhood wavelet shrinkage," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 404-416.
    4. Rivoirard, Vincent, 2004. "Maxisets for linear procedures," Statistics & Probability Letters, Elsevier, vol. 67(3), pages 267-275, April.
    5. 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).
    6. McGinnity, K. & Varbanov, R. & Chicken, E., 2017. "Cross-validated wavelet block thresholding for non-Gaussian errors," Computational Statistics & Data Analysis, Elsevier, vol. 106(C), pages 127-137.
    7. Fryzlewicz, Piotr & Nason, Guy P., 2004. "Smoothing the wavelet periodogram using the Haar-Fisz transform," LSE Research Online Documents on Economics 25231, London School of Economics and Political Science, LSE Library.
    8. Nilotpal Sanyal & Marco A. R. Ferreira, 2017. "Bayesian Wavelet Analysis Using Nonlocal Priors with an Application to fMRI Analysis," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(2), pages 361-388, November.
    9. Hee-Seok Oh & Donghoh Kim & Youngjo Lee, 2009. "Cross-validated wavelet shrinkage," Computational Statistics, Springer, vol. 24(3), pages 497-512, August.
    10. Chesneau, Christophe, 2007. "Regression with random design: A minimax study," Statistics & Probability Letters, Elsevier, vol. 77(1), pages 40-53, January.
    11. 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.
    12. Baqaee, David, 2010. "Using wavelets to measure core inflation: The case of New Zealand," The North American Journal of Economics and Finance, Elsevier, vol. 21(3), pages 241-255, December.
    13. 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.
    14. Durastanti, Claudio, 2016. "Adaptive global thresholding on the sphere," Journal of Multivariate Analysis, Elsevier, vol. 151(C), pages 110-132.
    15. Fryzlewicz, Piotr, 2007. "Bivariate hard thresholding in wavelet function estimation," LSE Research Online Documents on Economics 25219, London School of Economics and Political Science, LSE Library.
    16. Joachim Engel, 1997. "The multiresolution histogram," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 46(1), pages 41-57, January.
    17. Autin, F. & Freyermuth, Jean-Marc & von Sachs, Rainer, 2011. "Ideal denoising within a family of tree-structured wavelet estimators," LIDAM Discussion Papers ISBA 2011002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    18. Chesneau, Christophe, 2008. "On the maxiset comparison between hard and block thresholding methods," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 675-681, April.
    19. Peng, Jingfu, 2023. "Adaptive and efficient estimation in the Gaussian sequence model," Statistics & Probability Letters, Elsevier, vol. 195(C).
    20. 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.

    More about this item

    Statistics

    Access and download statistics

    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:taf:gnstxx:v:24:y:2012:i:4:p:905-922. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/GNST20 .

    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.