AI 中文总结
本文提出一种似然比检验，用于验证弱随机传递性不成立的原假设，证明其尺寸收敛性和功效性质，并通过模拟验证其有效性。
AI 中文摘要
本文提出并研究了一种似然比检验，其原假设为弱随机传递性（WST）不成立。这与文献中通常将WST设为原假设的表述相反。我们证明，即使当项目数量随每对比较次数增长时，均匀尺寸收敛于名义水平，其临界值由卡方平方分布确定。我们进一步证明，在足够的信号强度条件下，第二类错误均匀收敛于零。模拟研究展示了良好的有限样本第一类错误控制，并表明检验功效随样本量和信号强度的增加而提高。
英文摘要
This paper proposes and studies a likelihood-ratio test of the null hypothesis that weak stochastic transitivity (WST) does not hold. This is the reverse of the formulation commonly used in the literature, where WST is set as the null hypothesis. We show that, even when the number of items grows with the number of comparisons per pair, the uniform size converges to the nominal level, with the critical value determined by a chi-bar-square distribution. We further establish that the Type II error converges uniformly to zero under a sufficient signal-strength condition. Simulation studies demonstrate good finite-sample Type I error control and show that power increases with the sample size and signal strength.
