IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v103y1999i2d10.1023_a1021704903284.html
   My bibliography  Save this article

An Isotonic Regression Problem for Infinite-Dimensional Parameters

Author

Listed:
  • R. Khattree

    (Oakland University)

  • D. P. Schmidt

    (Oakland University)

  • I. E. Schochetman

    (Oakland University)

Abstract

We consider an infinite-dimensional isotonic regression problem which is an extension of the suitably revised classical isotonic regression problem. Given p-summable data, for p finite and at least one, there exists an optimal estimator to our problem. For p greater than one, this estimator is unique and is the limit in the p-norm of the sequence of unique estimators in canonical finite-dimensional truncations of our problem. However, for p equal to one, our problem, as well as the finite-dimensional truncations, admit multiple optimal estimators in general. In this case, the sequence of optimal estimator sets to the truncations converges to the optimal estimator set of the infinite problem in the sense of Kuratowski. Moreover, the selection of natural best optimal estimators to the truncations converges in the 1-norm to an optimal estimator of the infinite problem.

Suggested Citation

  • R. Khattree & D. P. Schmidt & I. E. Schochetman, 1999. "An Isotonic Regression Problem for Infinite-Dimensional Parameters," Journal of Optimization Theory and Applications, Springer, vol. 103(2), pages 359-384, November.
    • Handle: RePEc:spr:joptap:v:103:y:1999:i:2:d:10.1023_a:1021704903284
    DOI: 10.1023/A:1021704903284
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1021704903284
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1021704903284?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. Chakravarti, Nilotpal, 1989. "Bounded isotonic median regression," Computational Statistics & Data Analysis, Elsevier, vol. 8(2), pages 135-142, July.
    2. Menendez, J. A. & Salvador, B., 1987. "An algorithm for isotonic median regression," Computational Statistics & Data Analysis, Elsevier, vol. 5(4), pages 399-406, September.
    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. Ravindra K. Ahuja & James B. Orlin, 2001. "A Fast Scaling Algorithm for Minimizing Separable Convex Functions Subject to Chain Constraints," Operations Research, INFORMS, vol. 49(5), pages 784-789, October.
    2. Nilotpal Chakravarti, 1992. "Isotonic median regression for orders representable by rooted trees," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(5), pages 599-611, August.
    3. Ahuja, Ravindra K., 1956- & Orlin, James B., 1953-, 1997. "Solving the convex ordered set problem," Working papers WP 3988-97., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    4. Garren Steven T., 2003. "Improved estimation of medians subject to order restrictions in unimodal symmetric families," Statistics & Risk Modeling, De Gruyter, vol. 21(4/2003), pages 367-380, April.

    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:spr:joptap:v:103:y:1999:i:2:d:10.1023_a:1021704903284. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.