Controlling the false discovery rate (FDR) in variable selection becomes challenging when predictors are correlated, as existing methods often exclude all members of correlated groups and consequently perform poorly for prediction. We introduce a new setwise variable-selection framework that identifies clusters of potential predictors rather than forcing selection of a single variable. By allowing any member of a selected set to serve as a surrogate predictor, our approach supports strong predictive performance while maintaining rigorous FDR control. We construct sets via hierarchical clustering of predictors based on correlation, then test whether each set contains any non-null effects. Similar clustering and setwise selection have been applied in the familywise error rate (FWER) control regime, but previous research has been unable to overcome the inherent challenges of extending this to the FDR control framework. To control the FDR, we develop substantial generalizations of linear step-up procedures, extending the Benjamini-Hochberg and Benjamini-Yekutieli methods to accommodate the logical dependencies among these composite hypotheses. We prove that these procedures control the FDR at the nominal level and highlight their broader applicability. Simulation studies and real-data analyses show that our methods achieve higher power than existing approaches while preserving FDR control, yielding more informative variable selections and improved predictive models.

翻译：在变量选择中控制错误发现率（FDR）在预测变量相关时变得具有挑战性，因为现有方法通常会排除相关组的所有成员，从而导致预测性能不佳。我们提出了一种新的集合式变量选择框架，该框架识别潜在预测变量的聚类，而非强制选择单一变量。通过允许选定集合中的任何成员作为替代预测变量，我们的方法在保持严格FDR控制的同时支持强大的预测性能。我们基于相关性通过预测变量的层次聚类构建集合，然后检验每个集合是否包含任何非零效应。类似的聚类和集合式选择已在族错误率（FWER）控制体系中得到应用，但先前研究未能克服将其扩展到FDR控制框架的内在挑战。为控制FDR，我们发展了线性逐步提升程序的实质性推广，将Benjamini-Hochberg和Benjamini-Yekutieli方法扩展至适应这些复合假设间的逻辑依赖性。我们证明这些程序在名义水平上控制FDR，并强调其更广泛的适用性。模拟研究和实际数据分析表明，我们的方法在保持FDR控制的同时实现了比现有方法更高的统计功效，从而产生信息量更丰富的变量选择和改进的预测模型。