Implementing the jackknife

摘要

The jackknife is a well-known statistical procedure for bias reduction. It is given in terms of a ratio of two determinants. This ratio is exactly the same as in some sequence transformations used in numerical analysis for accelerating the convergence of a sequence by extrapolation. For such a transformation, a recursive algorithm for avoiding the computation of the determinants is known: the so-called E-algorithm. We show how properties of the jackknife follow from similar properties for the E-algorithm and how the E-algorithm can be used for implementing the jackknife.