Efron [J. Roy. Statist. Soc. Ser. B 54 (1992) 83–111] proposed a computationally efficient method, called the jackknife-after-bootstrap, for estimating the variance of a bootstrap estimator for independent data. For dependent data, a version of the jackknife-after-bootstrap method has been recently proposed by Lahiri [Econometric Theory 18 (2002) 79–98]. In this paper it is shown that the jackknife-after-bootstrap estimators of the variance of a bootstrap quantile are consistent for both dependent and independent data. Results from a simulation study are also presented.
"Consistency of the jackknife-after-bootstrap variance estimator for the bootstrap quantiles of a Studentized statistic." Ann. Statist. 33 (5) 2475 - 2506, October 2005. https://doi.org/10.1214/009053605000000507