Robust adaptive model selection and estimation for partial linear varying coefficient models in rank regression

Partial linear varying coefficient models are often used in real data analysis for a good balance between flexibility and parsimony. In this paper, we propose a robust adaptive model selection method based on the rank regression, which can do simultaneous coefficient estimation and three types of selections, i.e., varying and constant effects selection, relevant variable selection. The new method has superiority in robustness and efficiency by inheriting the advantage of the rank regression approach. Furthermore, consistency in the three types of selections and oracle property in estimation are established as well. Simulation studies also confirm our method.