标题： 学生t置信区间的覆盖误差，与Hall（1988）中的情况相当 显示英文标题

标题： Coverage errors for Student's t confidence intervals comparable to those in Hall (1988)

摘要： 表1来自Hall（1988）包含了一些基于$n$独立同分布样本的非参数近似95%置信区间的渐近覆盖误差公式。 该表包括了一个基于中心极限定理使用高斯分位数和高斯最大似然方差估计的区间条目。 它缺少了一个非常广泛使用的学生t$t$置信区间的条目。 本文对高斯条目进行了轻微的数值修正，并提供了学生t$t$区间的条目。 对于偏度$\gamma$和峰度$\kappa$，修正的高斯公式是$0.14\kappa -2.16\gamma^2-3.42$，而$t$区间的公式是$0.14\kappa -2.16\gamma^2$。 重新审视这个估计的动机来自于学生t统计量在随机准蒙特卡罗抽样中出人意料的稳健表现。 显示英文摘要

摘要： Table 1 of Hall (1988) contains asymptotic coverage error formulas for some nonparametric approximate 95% confidence intervals for the mean based on $n$ IID samples. The table includes an entry for an interval based on the central limit theorem using Gaussian quantiles and the Gaussian maximum likelihood variance estimate. It is missing an entry for the very widely used Student $t$ confidence intervals. This note makes a mild numerical correction for the Gaussian entry and provides an entry for the Student $t$ intervals. For skewness $\gamma$ and kurtosis $\kappa$, the corrected Gaussian formula is $0.14\kappa -2.16\gamma^2-3.42$ and the formula for the $t$ intervals is $0.14\kappa -2.16\gamma^2$. The impetus to revisit this estimate arose from the surprisingly robust performance of Student's t statistic in randomized quasi-Monte Carlo sampling.