摘要：We consider the problem of estimating an arbitrary smooth functional of k ≥ 1 distri-bution functions (d.f.s) in terms of random samples from them. The natural estimatereplaces the d.f.s by their empirical d.f.s. Its bias is generally ～ n.1, where n is theminimum sample size, with a pthorder iterative estimate of bias ～ n.pfor any p.For p ≤ 4, we give an explicit estimate in terms of the first 2 p . 2 von Mises deriva-tives of the functional evaluated at the empirical d.f.s. These may be used to obtainunbiased estimates, where these exist and are of known form in terms of the samplesizes; our form for such unbiased estimates is much simpler than that obtained usingpolykays and tables of the symmetric functions. Examples include functions of amean vector (such as the ratio of two means and the inverse of a mean), standard de-viation, correlation, return times and exceedances. These pthorder estimates requireonly ～ n calculations. This is in sharp contrast with computationally intensive biasreduction methods such as the pthorder bootstrap and jackknife, which require ～ npcalculations
关键词：bias reduction; correlation; exceedances; multisample; multivariate; nonparametric;ratio of means; return times; standard deviation; von Mises derivatives
