IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v44y2017i4p649-666.html
   My bibliography  Save this article

A new Bayesian wavelet thresholding estimator of nonparametric regression

Author

Listed:
  • M. Afshari
  • F. Lak
  • B. Gholizadeh

Abstract

The methods of estimation of nonparametric regression function are quite common in statistical application. In this paper, the new Bayesian wavelet thresholding estimation is considered. The new mixture prior distributions for the estimation of nonparametric regression function by applying wavelet transformation are investigated. The reversible jump algorithm to obtain the appropriate prior distributions and value of thresholding is used. The performance of the proposed estimator is assessed with simulated data from well-known test functions by comparing the convergence rate of the proposed estimator with respect to another by evaluating the average mean square error and standard deviations. Finally by applying the developed method, density function of galaxy data is estimated.

Suggested Citation

  • M. Afshari & F. Lak & B. Gholizadeh, 2017. "A new Bayesian wavelet thresholding estimator of nonparametric regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(4), pages 649-666, March.
  • Handle: RePEc:taf:japsta:v:44:y:2017:i:4:p:649-666
    DOI: 10.1080/02664763.2016.1182130
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/02664763.2016.1182130
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/02664763.2016.1182130?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. repec:dau:papers:123456789/1908 is not listed on IDEAS
    2. F. Abramovich & T. Sapatinas & B. W. Silverman, 1998. "Wavelet thresholding via a Bayesian approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(4), pages 725-749.
    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. Karamikabir, Hamid & Afshari, Mahmoud, 2020. "Generalized Bayesian shrinkage and wavelet estimation of location parameter for spherical distribution under balance-type loss: Minimaxity and admissibility," Journal of Multivariate Analysis, Elsevier, vol. 177(C).

    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. Marco Di Zio & Arnoldo Frigessi, 1999. "Smoothness in Bayesian Non-parametric Regression with Wavelets," Methodology and Computing in Applied Probability, Springer, vol. 1(4), pages 391-405, December.
    2. A. Antoniadis, 1997. "Rejoinder," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 6(2), pages 143-144, August.
    3. Matthieu Garcin & Dominique Guegan, 2015. "Optimal wavelet shrinkage of a noisy dynamical system with non-linear noise impact," Documents de travail du Centre d'Economie de la Sorbonne 15085, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    4. Mak Kaboudan, 2006. "Computational Forecasting of Wavelet-converted Monthly Sunspot Numbers," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(9), pages 925-941.
    5. Hee-Seok Oh & Donghoh Kim & Youngjo Lee, 2009. "Cross-validated wavelet shrinkage," Computational Statistics, Springer, vol. 24(3), pages 497-512, August.
    6. Capobianco Enrico & Marras Elisabetta & Travaglione Antonella, 2011. "Multiscale Characterization of Signaling Network Dynamics through Features," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 10(1), pages 1-32, November.
    7. Iolanda Lo Cascio, 2007. "Wavelet Analysis and Denoising: New Tools for Economists," Working Papers 600, Queen Mary University of London, School of Economics and Finance.
    8. Alex Rodrigo dos S. Sousa & Nancy L. Garcia & Brani Vidakovic, 2021. "Bayesian wavelet shrinkage with beta priors," Computational Statistics, Springer, vol. 36(2), pages 1341-1363, June.
    9. A. Antoniadis, 1997. "Wavelets in statistics: A review," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 6(2), pages 97-130, August.
    10. Haven, Emmanuel & Liu, Xiaoquan & Shen, Liya, 2012. "De-noising option prices with the wavelet method," European Journal of Operational Research, Elsevier, vol. 222(1), pages 104-112.
    11. ter Braak, Cajo J.F., 2006. "Bayesian sigmoid shrinkage with improper variance priors and an application to wavelet denoising," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1232-1242, November.
    12. Julyan Arbel & Ghislaine Gayraud & Judith Rousseau, 2013. "Bayesian Optimal Adaptive Estimation Using a Sieve prior," Working Papers 2013-19, Center for Research in Economics and Statistics.
    13. Abramovich, Felix & Besbeas, Panagiotis & Sapatinas, Theofanis, 2002. "Empirical Bayes approach to block wavelet function estimation," Computational Statistics & Data Analysis, Elsevier, vol. 39(4), pages 435-451, June.
    14. 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.
    15. Beran, Jan & Shumeyko, Yevgen, 2012. "Bootstrap testing for discontinuities under long-range dependence," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 322-347.
    16. Angelini, Claudia & De Canditiis, Daniela & Leblanc, Frédérique, 2003. "Wavelet regression estimation in nonparametric mixed effect models," Journal of Multivariate Analysis, Elsevier, vol. 85(2), pages 267-291, May.
    17. Natalia Bochkina & Theofanis Sapatinas, 2005. "On the posterior median estimators of possibly sparse sequences," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(2), pages 315-351, June.
    18. Yu Yue & Paul Speckman & Dongchu Sun, 2012. "Priors for Bayesian adaptive spline smoothing," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(3), pages 577-613, June.
    19. Beran, Jan & Heiler, Mark A., 2008. "A nonparametric regression cross spectrum for multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 99(4), pages 684-714, April.
    20. 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.

    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:japsta:v:44:y:2017:i:4:p:649-666. 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/CJAS20 .

    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.