Valliant, Richard L., J. Michael Brick, and Jill A. Dever. 2008. "Weight Adjustments for the Grouped Jackknife Variance Estimator." Journal of Official Statistics, 24(3): 469-488.
The jackknife variance estimator is often implemented by dropping groups of units rather than a single unit at a time. This has the practical advantages of economizing on computation time and file size because a separate weight is appended to the analysis file for each jackknife replicate. If the replicate weight adjustments and the grouped jackknife itself are not appropriately constructed, the variance estimates can have some extremely pathological behavior when estimating totals. When the dropout groups do not all have exactly the same number of first-stage units, the standard version of the grouped jackknife may be a severe overestimate. This problem is most likely to arise in single-stage samples with a large number of first-stage units in many of the strata. The standard grouped jackknife variance estimator and two alternatives are examined for the situation of unequally sized groups through a simulation study of school districts in the 50 United States and the District of Columbia.