We use the probabilistic method to show that if $f_{nh}$ is the standard kernel estimate with smoothing factor $h$, then there exists a deterministic sequence $h_n$ such that, for all densities, $\operatornamewithlimits{\lim\inf}_{n\rightarrow\infty} \frac{\mathbf{E} \int |f_{nh_n} - f|}{\inf_h \mathbf{E} \int |f_{nh} - f|} = 1.$
Publié le : 1994-06-14
Classification:
Density estimation,
kernel estimate,
probabilistic method,
nonparametric methods,
smoothing,
62G07,
62G05,
62F12,
60F25
@article{1176325500,
author = {Devroye, Luc},
title = {On Good Deterministic Smoothing Sequences for Kernel Density Estimates},
journal = {Ann. Statist.},
volume = {22},
number = {1},
year = {1994},
pages = { 886-889},
language = {en},
url = {http://dml.mathdoc.fr/item/1176325500}
}
Devroye, Luc. On Good Deterministic Smoothing Sequences for Kernel Density Estimates. Ann. Statist., Tome 22 (1994) no. 1, pp. 886-889. http://gdmltest.u-ga.fr/item/1176325500/