Semiparametric local variable selection under misspecification
针对半参数方法在非线性效应和模型误设定下易产生高假阳性率的问题，提出基于正交切割样条的方法，实现稳健的局部变量选择，适用于连续和分类协变量，并处理高维和相依数据。
Summary 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 nonlinear effects and model misspecification. Specifically, for common semiparametric 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 method 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, can handle both continuous and categorical covariates, and provides theory for high-dimensional covariates and model misspecification. We discuss settings with either independent or dependent data. The proposed method allows inclusion of 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 elucidate the effects of covariates on functional data measuring brain activation at different times.