On Inconsistency of the Jackknife-after-Bootstrap Bias Estimator for Dependent Data

B. Efron introducedjackknife-after-bootstrapas a computationally efficient method for estimating standard errors of bootstrap estimators. In a recent paper consistency of the jackknife-after-bootstrap variance estimators has been established for different bootstrap quantities for independent and dependent data. In this paper, it is shown that in the dependent case, the standard jackknife-after-bootstrap estimator for the bias of block bootstrap quantities is inconsistent for almost any sensible choice of the blocking parameters. Some alternative bias estimators are proposed and shown to be consistent.