Strategic two-sample test via the two-armed bandit process
提出一种基于双臂赌博机过程的策略性双样本检验统计量，通过打破数据可交换性来整合数据，相比经典方法在零假设下更集中、备择假设下更分散，从而提升检验功效。
Abstract This study aims to improve the power of two-sample tests by analysing whether the difference between two population parameters is larger than a prespecified positive equivalence margin. The classic test statistic treats the original data as exchangeable, while the proposed test statistic breaks the structure and proposes employing a two-armed bandit process to strategically integrate the data and thus a strategy-specific test statistic is constructed by combining the classic CLT with the law of large numbers. The developed asymptotic theory is investigated by using nonlinear limit theory in a larger probability space and relates to the ‘strategic CLT’ with a clearly defined density function. The asymptotic distribution demonstrates that the proposed statistic is more concentrated under the null hypothesis and less concentrated under the alternative than the classic CLT, thereby enhancing the testing power. Simulation studies provide supporting evidence for the theoretical results and portray a more powerful performance when using finite samples. A real example is also added for illustration.