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Weighted uniform consistency of kernel density estimators with general bandwidth sequences


 
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1. Title Title of document Weighted uniform consistency of kernel density estimators with general bandwidth sequences
 
2. Creator Author's name, affiliation, country Julia Dony; Free University of Brussels (VUB)
 
2. Creator Author's name, affiliation, country Uwe Einmahl; Free University of Brussels (VUB)
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) kernel density estimator; weighted uniform consistency; convergence rates; uniform in bandwidth; empirical process
 
3. Subject Subject classification 60B12, 60F15, 62G07
 
4. Description Abstract Let $f_{n,h}$ be a kernel density estimator of a continuous and bounded $d$-dimensional density $f$. Let $\psi(t)$ be a positive continuous function such that $\|\psi f^\beta\| _\infty < \infty$ for some $0< \beta < 1/2$. We are interested in the rate of consistency of such estimators with respect to the weighted sup-norm determined by $\psi$. This problem has been considered by Gin, Koltchinskii and Zinn (2004) for a deterministic bandwidth $h_n$. We provide ``uniform in $h$'' versions of some of their results, allowing us to determine the corresponding rates of consistency for kernel density estimators where the bandwidth sequences may depend on the data and/or the location.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Institute for the Promotion of Innovation through Science and Technology in Flanders (IWT-Vlaanderen), FWO-Vlaanderen
 
7. Date (YYYY-MM-DD) 2006-09-24
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/354
 
10. Identifier Digital Object Identifier 10.1214/EJP.v11-354
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 11
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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