This note studies the asymptotic behavior of the delete-$d$ jackknife in the irregular case of a sample $p$-quantile, calculated from a sample of $n$ iid r.v.'s. Two results are obtained: (a) an almost sure rate of convergence of the delete-$d$ jackknife histogram to the normal distribution; (b) almost sure convergence of the delete-$d$ jackknife variance estimate to the asymptotic variance of the sample $p$-quantile.
@article{1176347996,
author = {Shi, Xiquan},
title = {Some Asymptotic Results for Jackknifing the Sample Quantile},
journal = {Ann. Statist.},
volume = {19},
number = {1},
year = {1991},
pages = { 496-503},
language = {en},
url = {http://dml.mathdoc.fr/item/1176347996}
}
Shi, Xiquan. Some Asymptotic Results for Jackknifing the Sample Quantile. Ann. Statist., Tome 19 (1991) no. 1, pp. 496-503. http://gdmltest.u-ga.fr/item/1176347996/