Convergence in the Hausdorff metric of estimators of irregular densities, using Fourier-Cesàro approximation
The problem of estimating a density which is allowed to have discontinuities of the first kind is considered. The usual Fourier-type estimator is based on the Dirichlet or sine kernel and is not suitable to eliminate the Gibbs phenomenon. Fourier-Cesàro approximation yields the Fejér kernel which is the square of the sine function. Density estimators based on the Fejér kernel do control the Gibbs phenomenon. Integral metrics are not sufficiently sensitive to properly assess the performance of estimators of irregular signals. Therefore, we use the Hausdorff distance between the extended, closed, graphs of estimator and estimand, and derive an a.s. speed of convergence of this distance.
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.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 39 (1998)
Issue (Month): 2 (August)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:39:y:1998:i:2:p:179-184. 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: (Zhang, Lei)
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.