Composite Quantile Regression for the Single-Index Model

Abstract

In this paper, we use a projection based model specification. A balance between statistical precision and variable selection may be achieved by combining semiparametric ideas with variable selection techniques. More precisely, we pursue a single index strategy in combination with some variable selection methods that are applicable to a variety of calibration situations including conditional value at risk estimation. Moreover, the weighted composite loss function we consider is a flexible estimation framework to address the robustness and efficiency questions. In the setting with the dimensionality much larger than the sample size, we derive theoretical results on the asymptotic behavior of our estimation. The methodology is evaluated further in simulations and real data examples. Keywords and phrases: Quantile Single-index Regression; Minimum Average Contrast Estimation; Labor Economics; Composite quasi-maximum likelihood estimation; Lasso; Model selection.