论文标题
与仿制的可变选择：复合零假设
Variable Selection with the Knockoffs: Composite Null Hypotheses
论文作者
论文摘要
固定X仿型滤波器是一个灵活的框架，用于在具有任意设计矩阵（完整列等级）的线性模型中使用错误发现率（FDR）控制的可变框架，并且可以通过LASSO估计进行有限的样本选择性推断。在本文中，我们将仿冒程序的理论扩展到了复合零假设的测试，这些假设通常与现实世界中的问题更相关。主要的技术挑战在于与任意设计的相关特征同时处理复合零。我们开发了两种与仿制推断的方法，即仿制的普通最小二乘（S-OL）和特征反应产物扰动（FRPP），这些方法是建立在复合无效下测试统计量的新结构特性上的。我们还提出了S-OLS方法的两种启发式变体，以优于著名的Benjamini-Hochberg（BH）复合效应程序，该程序是依赖性测试统计量的启发式基线。最后，当原始的仿制程序被天真地应用于复合测试时，我们分析了FDR中的损失。
The fixed-X knockoff filter is a flexible framework for variable selection with false discovery rate (FDR) control in linear models with arbitrary design matrices (of full column rank) and it allows for finite-sample selective inference via the Lasso estimates. In this paper, we extend the theory of the knockoff procedure to tests with composite null hypotheses, which are usually more relevant to real-world problems. The main technical challenge lies in handling composite nulls in tandem with dependent features from arbitrary designs. We develop two methods for composite inference with the knockoffs, namely, shifted ordinary least-squares (S-OLS) and feature-response product perturbation (FRPP), building on new structural properties of test statistics under composite nulls. We also propose two heuristic variants of S-OLS method that outperform the celebrated Benjamini-Hochberg (BH) procedure for composite nulls, which serves as a heuristic baseline under dependent test statistics. Finally, we analyze the loss in FDR when the original knockoff procedure is naively applied on composite tests.
