Weighted composite quantile regression estimation and variable selection for varying coefficient models with heteroscedasticity

In this paper, we propose a data-driven penalized weighted composite quantile regression estimation for varying coefficient models with heteroscedasticity, which results in sparse and robust estimators simultaneously. With local weighted composite quantile regression smoothing and adaptive group LASSO, the new method can identify the true model and estimate the coefficient functions and heteroscedasticity simultaneously. The resulting estimators can be as efficient as the oracle estimators by using the SIC criterion to select the tuning parameters. In addition, we revise a mistake of Theorem 2 in Guo, Tian, and Zhu (2012). The finite sample performance of the newly proposed method is investigated through simulation studies and a real data example.