Variable Selection in Nonparametric Additive Models via Data Splitting

ABSTRACTIn high‐dimensional regression settings, variable selection remains a crucial challenge, particularly in the nonparametric additive models. Traditional methods for variable selection in the nonparametric additive models have focused on ensuring selection consistency, which aims to identify significant variables without misclassification. However, recent research trends acknowledge that significant variables may not be entirely separable from noise or insignificant variables and emphasize the importance of accepting some misclassification errors among selected variables. This paper proposes a novel approach that employs the multiple data splitting (MDS) method to select variables in the nonparametric additive models while controlling the false discovery rate (FDR). Our method constructs mirror statistics using the properties of inner products, allowing for measuring variable importance scores even when there are multiple coefficients with varying signs. Through simulation studies and a real data application, we show that our method has superior power in variable selection compared to traditional methods, such as the kernel knockoffs (KKO) and sparse additive models (SpAM) me