Power Robustification of Approximately Linear Tests
近似线性检验的功效稳健化AI 解读 ↓
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近似线性检验的功效稳健化
- 研究问题
- 当备择变化不仅是分布位置平移，还包含形状改变时，如何增强线性或近似线性检验的功效并减少平移情形的损失？
- 方法与思路
- 作者结合位置的线性统计量与形状的二次统计量构造贝叶斯漏斗检验，先在高斯框架分析，再用于两样本非线性秩检验。
- 材料陈述的贡献
- 摘要称，漏斗检验具有特定区域上的最大最小性质，在形状变化时增加功效而对平移备择损失较小，并报告模拟支持。
- 阅读关注点
- 应核对贝叶斯构造、不变性要求、功效展开与旋转锥区域的定义，以及高斯近似转入有限样本时的条件和模拟设定。
- 阅读边界
- 依据 OpenAlex 索引摘要，稿件版本未注明；摘要未量化功效收益与损失，最大最小性质也受指定区域限制，不能推断刊本变化。
原文摘要
We present a general method of improving the power of linear and approximately linear tests when deviations from a translation family of distributions must be taken into account. This method involves the combination of a linear statistic measuring location and a quadratic statistic measuring change of shape of the underlying distribution. The tests (“funnel tests”) are constructed as certain Bayes tests. In general they gain a sizeable amount of power over the linear tests adapted to the translation family when a change of shape of the underlying distribution occurs, while losing little for translation alternatives (“power robustification”). We introduce the concept of funnel tests in an Gaussian framework first. The effect of power robustification is studied by means of a power function expansion, which applies to a large class of tests sharing a certain invariance property. The funnel tests are characterized by a maximin property over a region defined by a rotational cone. The idea of the construction is then carried over to a finite sample situation where the Gaussian model is used as an approximation. As a particular application, we construct power-robustified nonlinear rank tests in the standard two-sample situation. A simulation study demonstrates the good overall performance of these tests as compared to other nonlinear tests.