用于多重比较的Split Knockoffs：控制方向性错误发现率
Split Knockoffs for Multiple Comparisons: Controlling the Directional False Discovery Rate
AI总结：
针对多重比较中线性变换约束下方向性错误发现率难以控制的问题，提出结合变量分裂与样本分裂的扩展Split Knockoff方法，可有效控制该错误率，且在仿真和阿尔茨海默病分析、年龄比较场景中验证了有效性。
摘要：
假设检验中的多重比较在各类应用中常面临结构约束。例如，在阿尔茨海默病的结构磁共振成像研究中，研究重点不仅限于检查萎缩脑区，还包括解剖学相邻区域的比较。这些约束可建模为参数的线性变换，其中符号模式在估计方向效应中起着关键作用。这类问题涵盖总变分、小波变换、fused LASSO、趋势滤波等，在有效控制方向性错误发现率方面存在公开挑战。本文提出一种扩展的Split Knockoff方法，专门用于解决线性变换下的方向性错误发现率控制问题。我们的方法将严格的线性流形约束放宽到其邻域，采用了优化中常用的变量分裂技术。该方法产生了一种正交设计，对检验效能和方向性错误发现率控制均有增益。通过引入样本分裂方案，我们实现了对方向性错误发现率的有效控制，且随着放宽邻域的扩大，该错误率会显著降至零。为验证方法的有效性，我们开展了仿真实验，并将其应用于两个真实场景：阿尔茨海默病分析和人类年龄比较。
英文摘要：
Multiple comparisons in hypothesis testing often encounter structural constraints in various applications. For instance, in structural Magnetic Resonance Imaging for Alzheimer's Disease, the focus extends beyond examining atrophic brain regions to include comparisons of anatomically adjacent regions. These constraints can be modeled as linear transformations of parameters, where the sign patterns play a crucial role in estimating directional effects. This class of problems, encompassing total variations, wavelet transforms, fused LASSO, trend filtering, and more, presents an open challenge in effectively controlling the directional false discovery rate. In this paper, we propose an extended Split Knockoff method specifically designed to address the control of directional false discovery rate under linear transformations. Our proposed approach relaxes the stringent linear manifold constraint to its neighborhood, employing a variable splitting technique commonly used in optimization. This methodology yields an orthogonal design that benefits both power and directional false discovery rate control. By incorporating a sample splitting scheme, we achieve effective control of the directional false discovery rate, with a notable reduction to zero as the relaxed neighborhood expands. To demonstrate the efficacy of our method, we conduct simulation experiments and apply it to two real-world scenarios: Alzheimer's Disease analysis and human age comparisons.
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