IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v57y1996i2p191-214.html
   My bibliography  Save this article

Estimation of the Location of the Maximum of a Regression Function Using Extreme Order Statistics

Author

Listed:
  • Chen, Hung
  • Huang, Mong-Na Lo
  • Huang, Wen-Jang

Abstract

In this paper, we consider the problem of approximating the location,x0[set membership, variant]C, of a maximum of a regresion function,[theta](x), under certain weak assumptions on[theta]. HereCis a bounded interval inR. A specific algorithm considered in this paper is as follows. Taking a random sampleX1, ..., Xnfrom a distribution overC, we have (Xi, Yi), whereYiis the outcome of noisy measurement of[theta](Xi). Arrange theYi's in nondecreasing order and take the average of ther Xi's which are associated with therlargest order statistics ofYi. This average,x0, will then be used as an estimate ofx0. The utility of such an algorithm with fixed r is evaluated in this paper. To be specific, the convergence rates ofx0tox0are derived. Those rates will depend on the right tail of the noise distribution and the shape of[theta](·) nearx0.

Suggested Citation

  • Chen, Hung & Huang, Mong-Na Lo & Huang, Wen-Jang, 1996. "Estimation of the Location of the Maximum of a Regression Function Using Extreme Order Statistics," Journal of Multivariate Analysis, Elsevier, vol. 57(2), pages 191-214, May.
  • Handle: RePEc:eee:jmvana:v:57:y:1996:i:2:p:191-214
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(96)90029-9
    Download Restriction: Full text for ScienceDirect subscribers only

    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. Dielman, Terry E. & Rose, Elizabeth L., 1996. "A note on hypothesis testing in LAV multiple regression: A small sample comparison," Computational Statistics & Data Analysis, Elsevier, vol. 21(4), pages 463-470, April.
    2. Dielman, Terry E. & Rose, Elizabeth L., 1995. "A bootstrap approach to hypothesis testing in least absolute value regression," Computational Statistics & Data Analysis, Elsevier, vol. 20(2), pages 119-130, August.
    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. Carlos A. Flores, 2007. "Estimation of Dose-Response Functions and Optimal Doses with a Continuous Treatment," Working Papers 0707, University of Miami, Department of Economics.
    2. Facer, Matthew R. & Müller, Hans-Georg, 2003. "Nonparametric estimation of the location of a maximum in a response surface," Journal of Multivariate Analysis, Elsevier, vol. 87(1), pages 191-217, October.
    3. Bai, Zhidong & Chen, Zehua & Wu, Yaohua, 2003. "Convergence rate of the best-r-point-average estimator for the maximizer of a nonparametric regression function," Journal of Multivariate Analysis, Elsevier, vol. 84(2), pages 319-334, February.

    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:eee:jmvana:v:57:y:1996:i:2:p:191-214. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.