IDEAS home Printed from
   My bibliography  Save this article

Maximin Estimation of Multidimensional Boundaries


  • Muller, H. G.
  • Song, K. S.


We consider the problem of estimating the location and size of a discontinuity in an otherwise smooth multidimensional regression function. The boundary or location of the discontinuity is assumed to be a closed curve respective surface, and we aim to estimate this closed set. Our approach utilizes the uniform convergence of multivariate kernel estimators for directional limits. Differences of such limits converge to zero under smoothness assumptions, and to the jump size along the discontinuity. This leads to the proposal of a maximin estimator, which selects the boundary for which the minimal estimated directional difference among all points belonging to this boundary is maximized. It is shown that this estimated boundary is almost surely enclosed in a sequence of shrinking neighborhoods around the true boundary, and corresponding rates of convergence are obtained.

Suggested Citation

  • Muller, H. G. & Song, K. S., 1994. "Maximin Estimation of Multidimensional Boundaries," Journal of Multivariate Analysis, Elsevier, vol. 50(2), pages 265-281, August.
  • Handle: RePEc:eee:jmvana:v:50:y:1994:i:2:p:265-281

    Download full text from publisher

    File URL:
    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.


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Polzehl, Jörg & Spokojnyj, Vladimir G., 1998. "Image denoising: Pointwise adaptive approach," SFB 373 Discussion Papers 1998,38, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    2. Garlipp, T. & Muller, C.H., 2006. "Detection of linear and circular shapes in image analysis," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1479-1490, December.
    3. Peihua Qiu, 2009. "Jump-preserving surface reconstruction from noisy data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(3), pages 715-751, September.
    4. Cheng, Ming-Yen & Hall, Peter, 2006. "Methods for tracking support boundaries with corners," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1870-1893, September.
    5. Delgado, Miguel A. & Hidalgo, Javier, 2000. "Nonparametric inference on structural breaks," Journal of Econometrics, Elsevier, vol. 96(1), pages 113-144, May.

    More about this item


    Access and download statistics


    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:50:y:1994:i:2:p:265-281. 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: .

    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.