Jackknifing under a budget constraint

In this paper, we consider the problem of estimating a parameter α that can be expressed as a nonlinear function of sample means. We develop a jackknife estimator for α that is appropriate to computational settings in which the total computer budget to be used is constrained. Despite the fact that the jackknifed observations are not i.i.d., we are able to show that our jackknife estimator reduces bias without increasing asymptotic variance. This makes the estimator particularly suitable for small sample applications. Because a special case of this estimator problem is that of estimating a ratio of two means, the results in this paper are pertinent to regenerative steady-state simulations.