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|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Kerkyacharian, G. & Picard, D., 1992. "Density estimation in Besov spaces," Statistics & Probability Letters, Elsevier, vol. 13(1), pages 15-24, January.
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: (Dana Niculescu)
If references are entirely missing, you can add them using this form.