Studentized tests of independence: Random-lifter approach
学生化独立性检验：随机提升方法AI 解读 ↓
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学生化独立性检验：随机提升方法
- 研究问题
- 对具有复杂几何结构的随机对象，如何构造零假设下具有简单极限分布的独立性检验，以降低渐近校准的计算负担？
- 方法与思路
- 作者引入随机提升机制，构造新的关联度量与学生化统计量，利用退化 U 统计量的中心极限定理获得标准正态极限。
- 材料陈述的贡献
- 摘要称，该方法无需样本分割，具有标准正态零假设极限及极小极大性质，并在模拟和真实数据中保持有竞争力的功效。
- 阅读关注点
- 应核对随机提升机制与调节参数、退化统计量的极限条件、学生化的有效性，以及极小极大性质和功效比较的确切含义。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要；摘要未说明备择类、具体速率或数值结果，简单渐近分布不等于有限样本准确校准。
原文摘要
The exploration of associations between random objects with complex geometric structures has catalyzed the development of various novel statistical tests encompassing distance-based and kernel-based statistics. These methods have various strengths and limitations. One problem is that their test statistics tend to converge to asymptotic null distributions involving second-order Wiener chaos, which are hard to compute and need approximation or permutation techniques that use much computing power to build rejection regions. In this work, we take an entirely different and novel strategy by using the so-called “random-lifter.” This method is engineered to yield test statistics with the standard normal limit under null distributions without the need for sample splitting. In other words, we set our sights on having simple limiting distributions and finding the proper statistics through reverse engineering. We use the Central Limit Theorems (CLTs) for degenerate U-statistics derived from our novel association measures to do this. As a result, the asymptotic distributions of our proposed tests are straightforward to compute. Our test statistics also have the minimax property. We further substantiate that our method maintains competitive power against existing methods with minimal adjustments to constant factors. Both numerical simulations and real-data analysis corroborate the efficacy of the random-lifter method.