Abstract

In meta analysis, a diverse range of methods for combining multiple p-values have been applied throughout the scientific literature. For sparse signals where only a small proportion of the p-values are truly significant, a technique called higher criticism has previously been shown to have asymptotic consistency and more power than Fisher’s original method. However, higher criticism and other related methods can still lack power. Three new, simple to compute statistics are now proposed for detecting sparse signals, based on standardizing partial sums or products of p-value order statistics. The use of standardization is theoretically justified with results demonstrating asymptotic normality, and avoids the computational difficulties encountered when working with analytic forms of the distributions of the partial sums and products. In particular, the standardized partial product demonstrates more power than existing methods for both the standard Gaussian mixture model and a real data example from computer network modeling.

摘要

在荟萃分析中，在整个科学文献中应用了多种组合多个p值的方法。对于只有一小部分p值真正显着的稀疏信号，先前已证明一种称为更高批评的技术比 Fisher 的原始方法具有渐近一致性和更大的功效。然而，更高的批评和其他相关方法仍然缺乏力量。基于标准化p的部分和或乘积，现在提出了三种新的、易于计算的统计数据来检测稀疏信号-价值订单统计。标准化的使用在理论上是合理的，结果证明了渐近正态性，并且避免了在处理部分和和乘积分布的分析形式时遇到的计算困难。特别是，对于标准高斯混合模型和来自计算机网络建模的真实数据示例，标准化的部分乘积显示出比现有方法更强大的能力。