Robust and sparse learning of varying coefficient models with high-dimensional features

Varying coefficient model (VCM) is extensively used in various scientific fields due to its capability of capturing the changing structure predictors. Classical mean regression analysis often complicated existence skewed, heterogeneous and heavy-tailed data. For this purpose, work employs idea averaging introduces a novel comprehensive approach by incorporating quantile-adaptive weights across different quantile levels further improve both least square (LS) (QR) methods. The proposed procedure that adaptively takes advantage sparse nature input data can gain more efficiency be well adapted extreme event case high-dimensional setting. Motivated nice properties, we develop several robust methods reveal dynamic close-to-truth for VCM consistently uncover zero nonzero patterns discoveries. We provide new iterative algorithm proven asymptotic consistent attain optimal nonparametric convergence rate given regular conditions. These introduced procedures are highlighted with extensive simulation examples real analyses show their stronger predictive power compared LS, composite (CQR) QR