Data-driven most powerful tests are statistical hypothesis decision-making tools that deliver the greatest power against a fixed null hypothesis among all corresponding data-based tests of a given size. When the underlying data distributions are known, the likelihood ratio principle can be applied to conduct most powerful tests. Reversing this notion, we consider the following questions. (a) Assuming a test statistic, say T, is given, how can we transform T to improve the power of the test? (b) Can T be used to generate the most powerful test? (c) How does one compare test statistics with respect to an attribute of the desired most powerful decision-making procedure? To examine these questions, we propose one-to-one mapping of the term 'Most Powerful' to the distribution properties of a given test statistic via matching characterization. This form of characterization has practical applicability and aligns well with the general principle of sufficiency. Findings indicate that to improve a given test, we can employ relevant ancillary statistics that do not have changes in their distributions with respect to tested hypotheses. As an example, the present method is illustrated by modifying the usual t-test under nonparametric settings. Numerical studies based on generated data and a real-data set confirm that the proposed approach can be useful in practice.

翻译：数据驱动的最优检验是统计假设决策工具，在给定显著性水平下，相较于所有基于数据的检验，它们能在固定原假设下提供最大的检验功效。当底层数据分布已知时，可应用似然比原理构建最优检验。基于此逆命题，我们考虑以下问题：(a) 假设给定某个检验统计量T，如何变换T以提升检验功效？(b) T能否用于生成最优检验？(c) 如何根据期望的最优决策过程的属性比较不同检验统计量？为探究这些问题，我们通过匹配刻画方法，将"最优"这一概念与给定检验统计量的分布特性建立一一对应关系。这种刻画形式具有实际应用价值，且与充分性原则高度契合。研究发现，要改进给定检验，可利用相关辅助统计量——这些统计量在假设检验条件下的分布不发生改变。本文通过修改非参数设定下的常规t检验示例来阐明该方法。基于模拟数据和真实数据集的数值研究证实了所提方法在实际应用中的有效性。