The knockoff filter is a recent false discovery rate (FDR) control method for high-dimensional linear models. We point out that knockoff has three key components: ranking algorithm, augmented design, and symmetric statistic, and each component admits multiple choices. By considering various combinations of the three components, we obtain a collection of variants of knockoff. All these variants guarantee finite-sample FDR control, and our goal is to compare their power. We assume a Rare and Weak signal model on regression coefficients and compare the power of different variants of knockoff by deriving explicit formulas of false positive rate and false negative rate. Our results provide new insights on how to improve power when controlling FDR at a targeted level. We also compare the power of knockoff with its propotype - a method that uses the same ranking algorithm but has access to an ideal threshold. The comparison reveals the additional price one pays by finding a data-driven threshold to control FDR.

翻译：Knockoff滤波器是一种针对高维线性模型的最新错误发现率（FDR）控制方法。我们指出，knockoff包含三个关键组成部分：排序算法、增广设计和对称统计量，且每个组成部分均有多种选择。通过考虑三者的不同组合，我们得到了一系列knockoff变体。所有这些变体均能保证有限样本下的FDR控制，而我们的目标是比较它们的统计功效。我们假设回归系数服从稀有弱信号模型，并通过推导误报率和漏报率的显式公式，比较不同knockoff变体的功效。研究结果揭示了如何在目标FDR水平下提升统计功效的新见解。此外，我们将knockoff与使用相同排序算法且能获取理想阈值的原型方法进行了功效比较，该比较揭示了通过寻找数据驱动阈值来控制FDR所需付出的额外代价。