Some Asymptotic Results for Jackknifing the Sample Quantile
样本分位数删 d 刀切法的若干渐近结果
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.