A New Variable Selection and Estimation Algorithm for the High-Dimensional Quantile Single-Index Model

The single-index model (SIM) reveals the intricate relationship between the response variable and covariates, allowing for the consideration of potential heterogeneity and nonlinearity in the data, while also offering interpretability and flexibility. This paper concentrates on estimating the parameters and the unknown link function for the quantile SIM with high-dimensional covariates. We introduce a novel iterative algorithm that strikes a balance between estimation accuracy, computational efficiency, and adaptability to diverse datasets. The initial values for iteration and iteration termination conditions are also discussed. The finite sample performance is illustrated through a simulation study, demonstrating the advantages of our method in terms of accuracy and speed.