可微统计泛函之渐近方差的一致估计

CONSISTENT ESTIMATORS OF THE ASYMPTOTIC VARIANCES OF DIFFERENTIABLE STATISTICAL FUNCTIONALS

本文对可微的统计泛函的渐近方差提出一个修改了的Jackknife估计,并且证明此种修改了的Jackknife估计的一致性所需条件只比原先的Jackknife估计少许强一点,本文还考虑到此种修改了的Jackknife估计的计算问题。最后还给出一个例子,借以说明上述理论的应用。

Consistenoy of a slightly modified jackknife estimator of the asymptotio variance of a differentiable statistical functional is established. This modified jackknife estimator is shown to require less stringent eonditions for its consistency than the original jaokknife estimator in very general situations. The computation aspeot of the modified jackknife estimator is also eonsidered. An exampleis given to illustrate the application of the theory.