IDEAS home Printed from https://ideas.repec.org/a/hin/jnljps/403764.html
   My bibliography  Save this article

A General Result on the Mean Integrated Squared Error of the Hard Thresholding Wavelet Estimator under -Mixing Dependence

Author

Listed:
  • Christophe Chesneau

Abstract

We consider the estimation of an unknown function for weakly dependent data ( -mixing) in a general setting. Our contribution is theoretical: we prove that a hard thresholding wavelet estimator attains a sharp rate of convergence under the mean integrated squared error (MISE) over Besov balls without imposing too restrictive assumptions on the model. Applications are given for two types of inverse problems: the deconvolution density estimation and the density estimation in a GARCH-type model, both improve existing results in this dependent context. Another application concerns the regression model with random design.

Suggested Citation

  • Christophe Chesneau, 2014. "A General Result on the Mean Integrated Squared Error of the Hard Thresholding Wavelet Estimator under -Mixing Dependence," Journal of Probability and Statistics, Hindawi, vol. 2014, pages 1-12, January.
    • Handle: RePEc:hin:jnljps:403764
    DOI: 10.1155/2014/403764
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/JPS/2014/403764.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/JPS/2014/403764.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2014/403764?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
    ---><---

    Citations

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


    Cited by:

    1. Luz M. Gómez & Rogério F. Porto & Pedro A. Morettin, 2021. "Nonparametric regression with warped wavelets and strong mixing processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(6), pages 1203-1228, December.

    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:hin:jnljps:403764. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    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.