IDEAS home Printed from https://ideas.repec.org/a/jss/jstsof/v012i08.html
   My bibliography  Save this article

EbayesThresh: R Programs for Empirical Bayes Thresholding

Author

Listed:
  • Johnstone, Iain
  • Silverman, Bernard W.

Abstract

Suppose that a sequence of unknown parameters is observed sub ject to independent Gaussian noise. The EbayesThresh package in the S language implements a class of Empirical Bayes thresholding methods that can take advantage of possible sparsity in the sequence, to improve the quality of estimation. The prior for each parameter in the sequence is a mixture of an atom of probability at zero and a heavy-tailed density. Within the package, this can be either a Laplace (double exponential) density or else a mixture of normal distributions with tail behavior similar to the Cauchy distribution. The mixing weight, or sparsity parameter, is chosen automatically by marginal maximum likelihood. If estimation is carried out using the posterior median, this is a random thresholding procedure; the estimation can also be carried out using other thresholding rules with the same threshold, and the package provides the posterior mean, and hard and soft thresholding, as additional options. This paper reviews the method, and gives details (far beyond those previously published) of the calculations needed for implementing the procedures. It explains and motivates both the general methodology, and the use of the EbayesThresh package, through simulated and real data examples. When estimating the wavelet transform of an unknown function, it is appropriate to apply the method level by level to the transform of the observed data. The package can carry out these calculations for wavelet transforms obtained using various packages in R and S-PLUS. Details, including a motivating example, are presented, and the application of the method to image estimation is also explored. The final topic considered is the estimation of a single sequence that may become progressively sparser along the sequence. An iterated least squares isotone regression method allows for the choice of a threshold that depends monotonically on the order in which the observations are made. An alternative possibility, also discussed in detail, is a particular parametric dependence of the sparsity parameter on the position in the sequence.

Suggested Citation

  • Johnstone, Iain & Silverman, Bernard W., 2005. "EbayesThresh: R Programs for Empirical Bayes Thresholding," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 12(i08).
  • Handle: RePEc:jss:jstsof:v:012:i08
    DOI: http://hdl.handle.net/10.18637/jss.v012.i08
    as

    Download full text from publisher

    File URL: https://www.jstatsoft.org/index.php/jss/article/view/v012i08/v12i08.pdf
    Download Restriction: no

    File URL: https://libkey.io/http://hdl.handle.net/10.18637/jss.v012.i08?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. Park, Junyong, 2014. "Shrinkage estimator in normal mean vector estimation based on conditional maximum likelihood estimators," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 1-6.
    2. Reese, Simon & Li, Yushu, 2013. "Testing for Structural Breaks in the Presence of Data Perturbations: Impacts and Wavelet Based Improvements," Working Papers 2013:36, Lund University, Department of Economics.
    3. Kim, Donghoh & Oh, Hee-Seok, 2006. "CVTresh: R Package for Level-Dependent Cross-Validation Thresholding," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 15(i10).
    4. Fryzlewicz, Piotr & Delouille, V´eronique & Nason, Guy P., 2007. "GOES-8 X-ray sensor variance stabilization using the multiscale data-driven Haar-Fisz transform," LSE Research Online Documents on Economics 25221, London School of Economics and Political Science, LSE Library.
    5. Maarten Jansen & Guy P. Nason & B. W. Silverman, 2009. "Multiscale methods for data on graphs and irregular multidimensional situations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 97-125, January.
    6. Guy P. Nason & Daniel Bailey, 2008. "Estimating the intensity of conflict in Iraq," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(4), pages 899-914, October.
    7. Anirban Bhattacharya & Debdeep Pati & Natesh S. Pillai & David B. Dunson, 2015. "Dirichlet--Laplace Priors for Optimal Shrinkage," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1479-1490, 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:jss:jstsof:v:012:i08. 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: Christopher F. Baum (email available below). General contact details of provider: http://www.jstatsoft.org/ .

    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.