For estimating the proportion of false null hypotheses in multiple testing, a family of estimators by Storey (2002) is widely used in the applied and statistical literature, with many methods suggested for selecting the parameter $\lambda$. Inspired by change-point concepts, our new approach to the latter problem first approximates the $p$-value plot with a piecewise linear function with a single change-point and then selects the $p$-value at the change-point location as $\lambda$. Simulations show that our method has among the smallest RMSE across various settings, and we extend it to address the estimation in cases of superuniform $p$-values. We provide asymptotic theory for our estimator, relying on the theory of quantile processes. Additionally, we propose an application in the change-point literature and illustrate it using high-dimensional CNV data.

翻译：摘要：在多重检验中估计虚假零假设比例时，Storey（2002）提出的一族估计量在应用统计学文献中被广泛使用，且已有多种方法被建议用于参数λ的选择。受变点概念的启发，我们针对该问题提出的新方法首先将p值图近似为具有单一变点的分段线性函数，然后将变点位置对应的p值选为λ。模拟结果表明，我们的方法在各种设定下均具有最小的均方根误差之一，并且我们将其扩展至处理超均匀p值情况下的估计问题。基于分位过程理论，我们为所提估计量建立了渐近理论。此外，我们还在变点文献中提出了一项应用，并通过高维CNV数据进行了实例说明。