标题： 基于相对论的统计检验框架，由辅助统计量的独立性引导：方法论和非参数示例 显示英文标题

标题： A Relativity-Based Framework for Statistical Testing Guided by the Independence of Ancillary Statistics: Methodology and Nonparametric Illustrations

摘要： 本文介绍了一种决策理论框架，用于根据检验统计量与辅助统计量之间的关系来构建和评估检验统计量——这些辅助统计量在原假设和备择假设下的分布保持不变。 而不是仅仅关注最大化区分能力，所提出的方法强调减少检验统计量与相关辅助结构之间的依赖性。 我们证明，最小化这种依赖性可以产生最有力（MP）的过程。 建立了一个类似于Basu的独立性结果，并且我们证明某些MP统计量也描述了底层数据分布。 通过修改经典非参数检验的方法来说明该方法，包括Shapiro-Wilk检验、Anderson-Darling检验和Kolmogorov-Smirnov检验，以及对称中心的检验。 模拟研究突出了所提出过程的效力和稳健性。 该框架计算简单，并为改进统计检验提供了一个有原则的策略。 显示英文摘要

摘要： This paper introduces a decision-theoretic framework for constructing and evaluating test statistics based on their relationship with ancillary statistics-quantities whose distributions remain fixed under the null and alternative hypotheses. Rather than focusing solely on maximizing discriminatory power, the proposed approach emphasizes reducing dependence between a test statistic and relevant ancillary structures. We show that minimizing such dependence can yield most powerful (MP) procedures. A Basu-type independence result is established, and we demonstrate that certain MP statistics also characterize the underlying data distribution. The methodology is illustrated through modifications of classical nonparametric tests, including the Shapiro-Wilk, Anderson-Darling, and Kolmogorov-Smirnov tests, as well as a test for the center of symmetry. Simulation studies highlight the power and robustness of the proposed procedures. The framework is computationally simple and offers a principled strategy for improving statistical testing.