Two step composite quantile regression for single-index models

This paper is concerned with composite quantile regression for single-index models. Under mild conditions, we show that the linear composite quantile regression offers a consistent estimate of the index parameter vector. With a root-nn consistent estimate of the index vector, the unknown link function can be estimated by local composite quantile regression. This procedure enables us to reduce the computational cost and is also appealing in high-dimensional data analysis. We show that the resulting estimator of the composite quantile function performs asymptotically as efficiently as if the true value of the index vector is known. The simulation studies and real data applications are conducted to illustrate the finite sample performance of the proposed methods.