IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this article

Exploring the use of variable bandwidth kernel density estimators

Listed author(s):
  • Isaias H. Salgado-Ugarte


    (F.E.S. Zaragoza U.N.A.M. Biologia)

  • Marco A. Perez-Hernandez


    (Depto. de Biologia, U.A.M. Iztapalapa, Mexico)

Variable bandwidth kernel density estimators increase the window width at low densities and decrease it where data concentrate. This represents an improvement over the fixed bandwidth kernel density estimators. In this article, we explore the use of one implementation of a variable kernel estimator in conjunction with several rules and procedures for bandwidth selection applied to several real datasets. The considered examples permit us to state that when working with tens or a few hundreds of data observations, least-squares cross-validation bandwidth rarely produces useful estimates; with thousands of observations, this problem can be surpassed. Optimal bandwidth and biased cross-validation (BCV), in general, oversmooth multimodal densities. The Sheather-Jones plug-in rule produced bandwidths that behave slightly better in this respect. The Silverman test is considered as a very sophisticated and safe procedure to estimate the number of modes in univariate distributions; however, similar results could be obtained with the Sheather-Jones rule, but at a much lower computational cost. As expected, the variable bandwidth kernel density estimates showed fewer modes than those chosen by the Silverman test, especially those distributions in which multimodality was caused by several noisy minor modes. More research on the subject is needed. Copyright 2003 by Stata Corporation.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL:
Download Restriction: no

File URL:
Download Restriction: no

Article provided by StataCorp LP in its journal Stata Journal.

Volume (Year): 3 (2003)
Issue (Month): 2 (June)
Pages: 133-147

in new window

Handle: RePEc:tsj:stataj:v:3:y:2003:i:2:p:133-147
Contact details of provider: Web page:

Order Information: Web:

No references listed on IDEAS
You can help add them by filling out this form.

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:tsj:stataj:v:3:y:2003:i:2:p:133-147. 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: (Christopher F. Baum)

or (Lisa Gilmore)

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.