Calibrating Confidence Coefficients
置信水平的校准AI 解读 ↓
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AI 根据所提供的论文材料归类：文本讨论置信区间覆盖率的一般校准理论，未提供所列经济计量细分方向的直接证据。
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置信水平的校准
- 研究问题
- 当标准置信区间的实际覆盖率偏离名义水平时，如何从数据估计并报告真实覆盖率，再据此调整区间以改善覆盖表现？
- 方法与思路
- 作者结合计算机模拟与密度估计来估计覆盖概率，再调整原区间的名义水平进行校准，并应用于总体方差和 bootstrap 区间。
- 材料陈述的贡献
- 摘要称，在若干常见情形证明渐近有效性；总体方差例子在六阶矩有限时具有覆盖率估计一致性及校准区间的渐近稳健性。
- 阅读关注点
- 应核对模拟与密度估计如何结合、校准水平如何求解，以及六阶矩条件对应哪些结果和新 bootstrap 区间的具体构造。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要；渐近结论不保证小样本覆盖，六阶矩条件也不能泛化为所有区间的统一充分条件。
原文摘要
Two approaches for dealing with the problem of poor coverage probabilities of certain standard confidence intervals are proposed. The first is a recommendation that the actual coverage be estimated directly from the data and its value reported in addition to the nominal level. This is achieved through a combination of computer simulation and density estimation. The asymptotic validity of the procedure is proved for a number of common situations. A classical example is the nonparametric estimation of the variance of a population using the normal-theory interval. Here it is shown that the estimated coverage probability consistently estimates the true coverage probability if the population distribution possesses a finite sixth moment. The second approach is more traditional. It is a procedure for modifying an interval to yield improved coverage properties. Given a confidence interval, its estimated coverage probability obtained in the first approach is used to alter the nominal level of the interval. The interval with this modified nominal level is called a calibrated interval. In the case that the given interval is the normal-theory interval for the estimation of variance, the calibrated interval is proved to be asymptotically robust as long as sixth moments exist. As another application, the method is used to modify a bootstrap interval procedure for variance estimation. This leads to the derivation of a new bootstrap interval.