@article{EJP354,
author = {Julia Dony and Uwe Einmahl},
title = {Weighted uniform consistency of kernel density estimators with general bandwidth sequences},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {11},
year = {2006},
keywords = {kernel density estimator; weighted uniform consistency; convergence rates; uniform in bandwidth; empirical process},
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.},
pages = {no. 33, 844-859},
issn = {1083-6489},
doi = {10.1214/EJP.v11-354},
url = {http://ejp.ejpecp.org/article/view/354}}