A Test in the Presence of Nuisance Parameters
存在干扰参数时的检验AI 解读 ↓
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存在干扰参数时的检验
- 研究问题
- 当检验的 p 值依赖未知干扰参数时，如何利用样本对该参数的信息，减轻在整个参数空间取上确界造成的保守性。
- 方法与思路
- 作者在原假设下构造干扰参数置信域，在域内对相应 p 值取上确界并加上未覆盖概率，同时允许统计量依赖干扰参数。
- 材料陈述的贡献
- 摘要称，方法适用于序约束推断及更广问题，示例和模拟中优于传统保守程序，但具体改善指标与幅度未说明。
- 阅读关注点
- 应核对置信域的覆盖保证、附加未覆盖概率如何控制检验水平，以及依赖干扰参数的统计量如何构造和计算。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要；有效性条件、置信域选择及模拟细节未说明，不能推断其他版本变化。
原文摘要
We are interested in testing Ψ = 0 against an alternative in the presence of some nuisance parameter λ. The usual procedure for such problems is to use a test statistic that is a function of the data only. Let q(λ) denote the p-value at a given value λ. If q(λ) does not depend on λ, then in principle we can apply this procedure. However, a major difficulty that arises in many situations is that q(λ) depends on λ and therefore cannot be used as a p-value. In such cases, the usual approach is to define the p-value as the supremum of q(λ) over the nuisance parameter space. Because this approach ignores sample information about λ, it may be unnecessarily conservative; this is a serious problem in order restricted inference. To overcome this, I propose the following. Obtain, say, a 99% confidence region for λ under the null hypothesis. Now, for a given λ, let T(λ) be a test statistic and r(λ) be the p-value. The test procedure is to reject the null hypothesis if {0.01 + supremum of r(λ) over the 99% confidence region for λ} is less than the nominal level such as 0.05. In contrast to the usual procedure, an attractive feature of this procedure is that it allows us to choose a test statistic as a function of λ. A data example is used to illustrate the procedure in a simulation study I observed that this test performed better than the traditional conservative procedure. Although this approach was originally developed for order restricted inference problems, the main results have wide applicability.