Jackknifing Differentiable Statistical Functionals

SUMMARY The purpose of this paper is to give a general unified view of “how smooth” a statistic needs to be for the jackknife to work. We give general sufficient conditions for the jackknife to produce consistent bias and variance estimators, and for linear combinations of the pseudovalues to be asymptotically normal. Regularity conditions are stated in terms of the existence of strong Fréchet differentials of the functional version of the statistic being jackknifed.