Assessing the error in bootstrap estimates with dependent data

Bootstrap estimates, like most random variables, are subject to sampling variation. Efron and Tibshirani (1993) studied the variability in bootstrap estimates with independent data. Efron (1992) proposed the jackknife-after-bootstrap, a method for estimating the variability from the bootstrap samples themselves. We address the issue of studying the variability in bootstrap estimates for dependent data. We modify Efron's method to render it suitable to operate through the block bootstrap. A simulation study is carried out to investigate the consistency of the modified method. The performance of this method is judged by using the same setting as that used by Efron and Tibshirani (1993). Our results confirm that this method is reliable and has an advantage in the context of dependent data.[PUBLICATION ABSTRACT]