On Symmetric Bootstrap Confidence Intervals
本文证明在相当一般的条件下，对称百分位-t自助置信区间的覆盖误差为O(n⁻²)，优于等尾百分位-t区间的常数n⁻¹，且对称区间不一定更长。基于Edgeworth和Cornish-Fisher展开预测了对称区间更短且覆盖误差更小的情形，并通过模拟验证。
SUMMARY It is shown that in quite general circumstances, symmetric percentile-t bootstrap confidence intervals have coverage error O(n –2), where n denotes sample size. This compares with an error of roughly constant n –1 for equal-tailed percentile-t confidence intervals. It is also proved that symmetric intervals are not necessarily any longer than equal-tailed intervals. Arguments based on Edgeworth and Cornish–Fisher expansions are used to predict circumstances in which symmetric intervals will have at once shorter length and smaller coverage error than equal-tailed intervals. The effect of number of replications on interval length and coverage error is discussed. Theoretical conclusions are illustrated in a simulation study.