In this paper we derive a law of the logarithm for the maximal deviation between a kernel density estimator and the true underlying density function. Extensions to higher derivatives are included. The results are applied to get optimal window-widths with respect to almost sure uniform convergence.
Publié le : 1982-05-14
Classification:
Empirical distribution function,
kernel density estimator,
oscillation modulus,
higher derivatives,
optimal window-widths,
62G05,
60F15,
62E20
@article{1176993866,
author = {Stute, Winfried},
title = {A Law of the Logarithm for Kernel Density Estimators},
journal = {Ann. Probab.},
volume = {10},
number = {4},
year = {1982},
pages = { 414-422},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993866}
}
Stute, Winfried. A Law of the Logarithm for Kernel Density Estimators. Ann. Probab., Tome 10 (1982) no. 4, pp. 414-422. http://gdmltest.u-ga.fr/item/1176993866/