It turns out that for standard kernel estimators no inequality like that of Dvoretzky-Kiefer-Wolfowitz can be constructed, and as a result it is impossible to answer the question of how many observations are needed to guarantee a prescribed level of accuracy of the estimator. A remedy is to adapt the bandwidth to the sample at hand.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am34-4-3,
author = {Ryszard Zieli\'nski},
title = {Kernel estimators and the Dvoretzky-Kiefer-Wolfowitz inequality},
journal = {Applicationes Mathematicae},
volume = {34},
year = {2007},
pages = {401-404},
zbl = {1130.62031},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am34-4-3}
}
Ryszard Zieliński. Kernel estimators and the Dvoretzky-Kiefer-Wolfowitz inequality. Applicationes Mathematicae, Tome 34 (2007) pp. 401-404. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am34-4-3/