Though jackknifing serves well the dual purpose of bias reduction and variance estimation, the pseudovariables it generates may not generally preserve robustness for general statistical functionals. These pseudovariables are incorporated in a differentiable functional detour of jackknifing, and along with its rationality, the related asymptotic theory is studied systematically. A two-step jackknifing is considered for the variance estimation. Second-order asymptotic distributional representations for the classical jackknifed estimators are also considered.
"Functional Jackknifing: Rationality and General Asymptotics." Ann. Statist. 16 (1) 450 - 469, March, 1988. https://doi.org/10.1214/aos/1176350714