Two-Sided Tests and One-Sided Confidence Bounds
双侧检验与单侧置信界AI 解读 ↓
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双侧检验与单侧置信界
- 研究问题
- 当研究者仅在双侧检验拒绝原假设后关心参数偏离方向及偏离距离下界时，如何构造相应的单侧置信界？
- 方法与思路
- 作者利用检验与置信集的对偶性构造拒绝后的单侧界，并在单参数指数族、位置族及其他例子中研究该方法。
- 材料陈述的贡献
- 摘要称拒绝后新界不劣于双侧区间的对应界；真参数远离原假设时，新界趋近完整置信水平的单侧界。
- 阅读关注点
- 应核对拒绝后报告规则、方向判断和覆盖概率的定义，以及不劣性比较及与经典单侧界一致所需的条件。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要；未说明覆盖保证是无条件还是拒绝条件下的性质，不能自行补充选择后推断结论。
原文摘要
Based on the duality between tests and confidence sets we introduce a new method to derive one-sided confidence bounds following the rejection of a null hypothesis with two-sided alternatives. This method imputes that the experimenter is only interested in confidence bounds if the null hypothesis is rejected. Furthermore, we suppose that he is only interested in the direction and a lower confidence bound concerning the distance of the true parameter value to the parameter values in the null hypothesis. If the null hypothesis is rejected, the new one-sided confidence bounds are always not worse than the corresponding bounds of the two-sided confidence interval approach. If the true parameter is far away from the null hypothesis, the new bounds tend to be nearly equal to the corresponding one-sided confidence bounds with full confidence level $1 - \alpha$. The new method will be studied and illustrated in more detail in one-parameter exponential families and location families with unimodal Lebesgue densities, and, as an example where conditional tests are available, we consider the comparison of two Poission distributions. In case of the normal distribution with unknown variance we propose among others a modification of a procedure of Hodges and Lehmann. Here it may be surprising that there exist situations where the new method yields confidence bounds exactly matching the classical one-sided confidence bounds.