In this paper we obtain uniform upper bounds for the $L_1$ error of kernel estimators in estimating monotone densities and densities of bounded variation. The bounds are nonasymptotic and optimal in $n$, the sample size. For the bounded variation class, it is also optimal wrt an upper bound of the total variation. The proofs employ a one-sided kernel technique and are extremely simple.
Publié le : 1992-09-14
Classification:
Monotone density,
density of bounded variation,
$L_1$ estimation,
minimax risk,
kernel estimator,
nonasymptotic bound,
62G07,
62C20
@article{1176348791,
author = {Datta, Somnath},
title = {Some Nonasymptotic Bounds for $L\_1$ Density Estimation using Kernels},
journal = {Ann. Statist.},
volume = {20},
number = {1},
year = {1992},
pages = { 1658-1667},
language = {en},
url = {http://dml.mathdoc.fr/item/1176348791}
}
Datta, Somnath. Some Nonasymptotic Bounds for $L_1$ Density Estimation using Kernels. Ann. Statist., Tome 20 (1992) no. 1, pp. 1658-1667. http://gdmltest.u-ga.fr/item/1176348791/