The Efron-Stein inequality is applied to prove that the kernel density estimate $f_n$, with an arbitrary nonnegative kernel and an arbitrary smoothing factor, satisfies the inequality $\operatorname{var}(\int|f_n - f|) \leq 4/n$ for all densities $f$. Similar inequalities are obtained for other estimates.
Publié le : 1987-09-14
Classification:
Efron-Stein inequality,
density estimation,
kernel estimate,
distribution-free confidence interval,
60E15,
62G05
@article{1176350508,
author = {Devroye, Luc},
title = {An Application of the Efron-Stein Inequality in Density Estimation},
journal = {Ann. Statist.},
volume = {15},
number = {1},
year = {1987},
pages = { 1317-1320},
language = {en},
url = {http://dml.mathdoc.fr/item/1176350508}
}
Devroye, Luc. An Application of the Efron-Stein Inequality in Density Estimation. Ann. Statist., Tome 15 (1987) no. 1, pp. 1317-1320. http://gdmltest.u-ga.fr/item/1176350508/