Fast Estimators of the Jackknife

The jackknife is a reliable method for estimating standard error nonparametrically. The method is easy to use, but is computationally intensive. The time required to compute the jackknife standard error for an estimator will depend on the time required to compute itself. For some estimators the required time is prohibitive. This may be especially true in simulation studies where and its standard error are computed for a large number of datasets. Let X 1 , X 2 , ..., X N be a random sample and the estimator computed with X i removed. Then is the jackknife estimator of the variability of where . In this paper estimators of are defined that can be computed quickly while sacrificing little precision or accuracy. The method requires that random variables are available that can be computed quickly and are strongly correlated with . It is described how can generally be obtained, and the method is illustrated with two examples. The paper focuses on the jackknife estimator for standard error, but the method can also be applied to quickly compute the jackknife estimator of bias.