Under fairly general assumptions on the underlying distribution function, the bootstrap process, pertaining to the sample $q$-quantile, converges weakly in $D_\mathbb{R}$ to the standard Brownian motion. Furthermore, weak convergence of a smoothed bootstrap quantile estimate is proved which entails that in this particular case the smoothed bootstrap estimate outperforms the nonsmoothed one.
Publié le : 1989-01-14
Classification:
Sample quantile,
empirical distribution function,
bootstrap process,
Brownian motion,
kernel estimate,
62G30,
60F05,
60G99
@article{1176991515,
author = {Falk, M. and Reiss, R.-D.},
title = {Weak Convergence of Smoothed and Nonsmoothed Bootstrap Quantile Estimates},
journal = {Ann. Probab.},
volume = {17},
number = {4},
year = {1989},
pages = { 362-371},
language = {en},
url = {http://dml.mathdoc.fr/item/1176991515}
}
Falk, M.; Reiss, R.-D. Weak Convergence of Smoothed and Nonsmoothed Bootstrap Quantile Estimates. Ann. Probab., Tome 17 (1989) no. 4, pp. 362-371. http://gdmltest.u-ga.fr/item/1176991515/