IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v26y1988i1p59-88.html
   My bibliography  Save this article

Minimizing L1 distance in nonparametric density estimation

Author

Listed:
  • Hall, Peter
  • Wand, Matthew P.

Abstract

We construct a simple algorithm, based on Newton's method, which permits asymptotic minimization of L1 distance for nonparametric density estimators. The technique is applicable to multivariate kernel estimators, multivariate histogram estimators, and smoothed histogram estimators such as frequency polygons. It has an "adaptive" or "data-driven" version. We show theoretically that both theoretical and adaptive forms of the algorithm do indeed minimize asymptotic L1 distance. Then we apply the algorithm to derive concise formulae for asymptotically optimal smoothing parameters. We also give numerical examples of applications of the adaptive algorithm.

Suggested Citation

  • Hall, Peter & Wand, Matthew P., 1988. "Minimizing L1 distance in nonparametric density estimation," Journal of Multivariate Analysis, Elsevier, vol. 26(1), pages 59-88, July.
    • Handle: RePEc:eee:jmvana:v:26:y:1988:i:1:p:59-88
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0047-259X(88)90073-5
    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. Klemelä, Jussi, 2000. "Estimation of Densities and Derivatives of Densities with Directional Data," Journal of Multivariate Analysis, Elsevier, vol. 73(1), pages 18-40, April.
    2. Ouimet, Frédéric & Tolosana-Delgado, Raimon, 2022. "Asymptotic properties of Dirichlet kernel density estimators," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    3. Davies, P. Laurie & Gather, Ursula & Nordman, Daniel & Weinert, Henrike, 2007. "Constructing a regular histogram : a comparison of methods," Technical Reports 2007,14, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    4. Jizba, Petr & Korbel, Jan, 2014. "Multifractal diffusion entropy analysis: Optimal bin width of probability histograms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 438-458.
    5. Wang, Xiao-Feng & Ye, Deping, 2015. "Conditional density estimation in measurement error problems," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 38-50.
    6. Petr Jizba & Jan Korbel, 2014. "Multifractal Diffusion Entropy Analysis: Optimal Bin Width of Probability Histograms," Papers 1401.3316, arXiv.org, revised Mar 2014.

    More about this item

    Keywords

    asymptotic optimality histogram estimator kernel estimator L1 distance nonparametric density estimator;

    JEL classification:

    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

    Statistics

    Access and download statistics

    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:26:y:1988:i:1:p:59-88. 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.