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：在多重检验中估计错误零假设的比例时，Storey (2002) 提出的一系列估计量在应用与统计文献中广泛使用，并有许多方法被建议用于选择参数 $\lambda$。受变点概念启发，我们针对后一问题的新方法首先将 $p$ 值图近似为带有单个变点的分段线性函数，然后选取变点位置处的 $p$ 值作为 $\lambda$。模拟表明，我们的方法在不同设定下均具有最小的均方根误差之一，并且我们将其扩展到处理超均匀 $p$ 值情况下的估计问题。我们基于分位数过程理论为估计量提供了渐近理论。此外，我们在变点文献中提出了一项应用，并使用高维CNV数据进行了说明。