Jackknifing Variances

Abstract

1. Introduction. The Tukey jackknife [18], [19], [11], which is an extension of an idea of Quenouille [12], is a rough-and-ready statistical tool which (a) reduces bias and (b) produces approximate confidence intervals. It exactly eliminates a 1/n bias term. Its approximate confidence intervals are a godsend in problems where messy distribution theory prohibits the formation of exact confidence limits. It has been demonstrated that the jackknife can be beneficially applied in ratio problems (Quenouille [13], Durbin [6], Rao [14], Rao and Webster [15], Deming [5]), in maximum likelihood estimation (Brillinger [3]), and in transformations