In this article we derive a law of the logarithm for the maximal deviation between two kernel-type quantile density estimators and the true underlying quantile density function in the randomly right-censored case. Extensions to higher derivatives are included. The results are applied to get optimal bandwidths with respect to almost sure uniform convergence.
Publié le : 1994-04-14
Classification:
Quantile density function,
random censorship,
Kaplan-Meier estimator,
kernel quantile density estimator,
optimal bandwidths,
strong Gaussian approximation,
oscillation modulus,
60F15,
62G05,
62G30
@article{1176988741,
author = {Xiang, Xiaojing},
title = {A Law of the Logarithm for Kernel Quantile Density Estimators},
journal = {Ann. Probab.},
volume = {22},
number = {4},
year = {1994},
pages = { 1078-1091},
language = {en},
url = {http://dml.mathdoc.fr/item/1176988741}
}
Xiang, Xiaojing. A Law of the Logarithm for Kernel Quantile Density Estimators. Ann. Probab., Tome 22 (1994) no. 4, pp. 1078-1091. http://gdmltest.u-ga.fr/item/1176988741/