IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v70y1999i2p177-201.html
   My bibliography  Save this article

Nonparametric Regression with Singular Design

Author

Listed:
  • Lu, Zhan-Qian

Abstract

Theories of nonparametric regression are usually based on the assumption that the design density exists. However, in some applications such as those involving high-dimensional or chaotic time series data, the design measure may be singular and may be likely to have a fractal (nonintegral) dimension. In this paper, the popular Nadaraya-Watson estimator is studied under the general setup that the continuity of the design measure is governed by the local or pointwise dimension. It will be shown in the iid setup that the nonparametric regression estimator achieves a convergence rate which is dependent only on the pointwise dimension. The case of time series data is also studied. For the latter case, a new mixing condition is introduced, and an assumption of marginal or joint density is completely avoided. Three examples, a fractal regression and two applications for predicting chaotic time series, are used to illustrate the implications of the obtained results.

Suggested Citation

  • Lu, Zhan-Qian, 1999. "Nonparametric Regression with Singular Design," Journal of Multivariate Analysis, Elsevier, vol. 70(2), pages 177-201, August.
    • Handle: RePEc:eee:jmvana:v:70:y:1999:i:2:p:177-201
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(99)91813-4
    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

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


    Cited by:

    1. Z. Q. John Lu, 2010. "The Elements of Statistical Learning: Data Mining, Inference, and Prediction," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 173(3), pages 693-694, July.
    2. Nengxiang Ling & Shuhe Hu, 2008. "Asymptotic distribution of partitioning estimation and modified partitioning estimation for regression functions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(4), pages 353-363.
    3. Zinde-Walsh, Victoria, 2008. "Kernel Estimation When Density May Not Exist," Econometric Theory, Cambridge University Press, vol. 24(3), pages 696-725, June.

    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:70:y:1999:i:2:p:177-201. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.