This paper investigates the effectiveness of the first and second order jackknife estimators, as tools for bias reduction. The biases of the estimators are characterized in terms of the bias of the original estimator. The biases of the two estimators are compared asymptotically with each other and with the bias of the original estimator.
J. E. Adams. H. L. Gray. T. A. Watkins. "An Asymptotic Characterization of Bias Reduction By Jackknifing." Ann. Math. Statist. 42 (5) 1606 - 1612, October, 1971. https://doi.org/10.1214/aoms/1177693159