IDEAS home Printed from https://ideas.repec.org/a/bpj/strimo/v23y2005i3-2005p181-198n2.html
   My bibliography  Save this article

Empirical Bayes estimation by wavelet series

Author

Listed:
  • Pensky Marianna
  • Alotaibi Mohammed

Abstract

In traditional nonparametric EB (empirical Bayes) setting, the paper proposes generalization of the linear EB estimation method which takes advantage of the flexibility of the wavelet techniques. A nonparametric EB estimator is represented as a wavelet series expansion and the coefficients are estimated by minimizing the prior risk of the estimator. Although wavelet series have been used previously for EB estimation, the method suggested in the paper is completely novel since the EB estimator as a whole is represented as a wavelet series rather than its components. Moreover, the method exploits de-correlating property of wavelets which is not instrumental for the former wavelet-based EB techniques. As a result, estimation of wavelet coefficients requires solution of a well-posed sparse system of linear equations. The technique provides asymptotically optimal EB estimators posterior risks of which tend to zero at the optimal rate as the number of observations tends to infinity.

Suggested Citation

  • Pensky Marianna & Alotaibi Mohammed, 2005. "Empirical Bayes estimation by wavelet series," Statistics & Risk Modeling, De Gruyter, vol. 23(3), pages 181-198, March.
    • Handle: RePEc:bpj:strimo:v:23:y:2005:i:3/2005:p:181-198:n:2
    DOI: 10.1524/stnd.2005.23.3.181
    as

    Download full text from publisher

    File URL: https://doi.org/10.1524/stnd.2005.23.3.181
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1524/stnd.2005.23.3.181?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. Huang, Su-Yun, 1997. "Wavelet based empirical Bayes estimation for the uniform distribution," Statistics & Probability Letters, Elsevier, vol. 32(2), pages 141-146, March.
    2. Zhang, Shunpu & Karunamuni, Rohana J., 1997. "Bayes and empirical Bayes estimation with errors in variables," Statistics & Probability Letters, Elsevier, vol. 33(1), pages 23-34, April.
    3. Tiwari, Ram C. & Zalkikar, Jyoti N., 1990. "Empirical Bayes estimation of the scale parameter in a Pareto distribution," Computational Statistics & Data Analysis, Elsevier, vol. 10(3), pages 261-270, December.
    4. R. Singh & Laisheng Wei, 1992. "Empirical Bayes with rates and best rates of convergence in u(x)C(θ) exp(-x/θ)-family: Estimation case," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 44(3), pages 435-449, September.
    5. Marianna Pensky, 2002. "Locally Adaptive Wavelet Empirical Bayes Estimation of a Location Parameter," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(1), pages 83-99, March.
    Full references (including those not matched with items on IDEAS)

    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. Pensky Marianna, 2002. "A New Approach To Empirical Bayes Estimation With Errors In Variables," Statistics & Risk Modeling, De Gruyter, vol. 20(1-4), pages 225-240, April.
    2. Marianna Pensky, 2002. "Locally Adaptive Wavelet Empirical Bayes Estimation of a Location Parameter," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(1), pages 83-99, March.
    3. Huang, Wen-Tao & Huang, Hui-Hsin, 2006. "Empirical Bayes estimation of the guarantee lifetime in a two-parameter exponential distribution," Statistics & Probability Letters, Elsevier, vol. 76(16), pages 1821-1829, October.
    4. Arturo Fernández, 2008. "Highest posterior density estimation from multiply censored Pareto data," Statistical Papers, Springer, vol. 49(2), pages 333-341, April.
    5. Zhang, Shunpu & Karunamuni, Rohana J., 1997. "Bayes and empirical Bayes estimation with errors in variables," Statistics & Probability Letters, Elsevier, vol. 33(1), pages 23-34, April.
    6. Fernandez, Arturo J., 2006. "Bayesian estimation based on trimmed samples from Pareto populations," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1119-1130, November.
    7. Liang, TaChen, 2009. "Empirical Bayes estimation for Borel-Tanner distributions," Statistics & Probability Letters, Elsevier, vol. 79(20), pages 2212-2219, October.
    8. Fernández, Arturo J., 2013. "Smallest Pareto confidence regions and applications," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 11-25.

    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:bpj:strimo:v:23:y:2005:i:3/2005:p:181-198:n:2. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.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.