Local variable selection aims to test for the effect of covariates on an outcome within specific regions. We outline a challenge that arises in the presence of non-linear effects and model misspecification. Specifically, for common semi-parametric methods even slight model misspecification can result in a high false positive rate, in a manner that is highly sensitive to the chosen basis functions. We propose a methodology based on orthogonal cut splines that avoids false positive inflation for any choice of knots, and achieves consistent local variable selection. Our approach offers simplicity, handles both continuous and categorical covariates, and provides theory for high-dimensional covariates and model misspecification. We discuss settings with either independent or dependent data. Our proposal allows including adjustment covariates that do not undergo selection, enhancing the model's flexibility. Our examples describe salary gaps associated with various discrimination factors at different ages, and the effects of covariates on functional data measuring brain activation at different times.

翻译：局部变量选择旨在检验协变量在特定区域内对结果的影响。我们阐述了在存在非线性效应和模型误设时出现的一个挑战。具体而言，对于常见的半参数方法，即使轻微的模型误设也可能导致较高的假阳性率，且该现象对所选基函数极为敏感。我们提出了一种基于正交截断样条的方法，该方法能够避免任意节点选择导致的假阳性膨胀，并实现一致的局部变量选择。我们的方法具有简洁性，可同时处理连续型和分类型协变量，并为高维协变量和模型误设情况提供了理论支持。我们讨论了独立数据与相关数据两种设定。所提方法允许纳入不参与选择的调整协变量，从而增强了模型的灵活性。我们的示例描述了不同年龄阶段与各类歧视因素相关的薪资差距，以及协变量在不同时间点上对测量大脑激活的功能数据的影响。