最小离散性和最小随机化p值
Minimally Discrete and Minimally Randomized p-Values
AI总结：
本文提出最小离散和最小随机化p值，以提高p值构造效率并减少离散效应带来的负面影响。
摘要：
在荟萃分析、多重假设检验等方法中，p值被用作输入，并假设在原假设下p值在单位区间内均匀分布。如果生成p值的数据具有离散分布，则通常使用自然p值、中p值或随机化p值。自然和中p值可以在原假设下通过随机和凸序支配均匀分布，从而允许有效但保守的后续方法。随机化p值不需要导致保守的程序，因为它们通过生成独立的辅助变量来实现原假设下的均匀分布。然而，辅助变量必然增加程序的变异性。本文介绍了并研究了“最小离散”（MD）自然p值、MD中p值和“最小随机化”（MR）p值。研究表明，MD p值在随机和凸序上支配其非MD对应物，因此导致更不保守但仍有效的后续方法。同样，MR p值在非MR对应物中占据主导地位，因为它们在原假设下仍然均匀分布，但因独立生成的辅助变量带来的额外变异性更小。预计本文的结果将通过更高效的p值构造促进新的荟萃分析和多重检验方法的构建，并通过建立解决不可避免的有害“离散效应”的金标准，促进现有和新方法的理论研究。
英文摘要：
In meta analysis, multiple hypothesis testing and many other methods, p-values are utilized as inputs and assumed to be uniformly distributed over the unit interval under the null hypotheses. If data used to generate p-values have discrete distributions then either natural, mid- or randomized p-values are typically utilized. Natural and mid-p-values can allow for valid, albeit conservative, downstream methods since under the null hypothesis they are dominated by uniform distributions in the stochastic and convex order, respectively. Randomized p-values need not lead to conservative procedures since they permit a uniform distributions under the null hypotheses through the generation of independent auxiliary variates. However, the auxiliary variates necessarily add variation to procedures. This manuscript introduces and studies ``minimally discrete'' (MD) natural p-values, MD mid-p-values and ``minimally randomized'' (MR) p-values. It is shown that MD p-values dominate their non-MD counterparts in the stochastic and convex order, and hence lead to less conservative, yet still valid, downstream methods. Likewise, MR p-values dominate their non-MR counterparts in that they are still uniformly distributed under the null hypotheses, but the added variation attributable to the independently generated auxiliary variate is smaller. It is anticipated that results here will facilitate the construction of new meta-analysis and multiple testing methods via more efficient p-value construction, and facilitate theoretical study of existing and new methods by establishing gold standards for addressing the unavoidable detrimental ``discreteness effect''.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
