In general, high-dimensional data often display heterogeneity. If the heteroscedasticity is neglected in the regression model, it will produce inefficient inferences of the regression coefficients. Quantile regression is not only robust to outliers, but also accommodates the heterogeneity. We hence apply multiple quantiles regression to identify the heteroscedasticity, seek for common features of quantile coefficients and eliminate irrelevant variables simultaneously based on the regularized approach. We also give the theoretical properties of the proposed method under some regularity conditions. Simulation studies are conducted to illustrate the finite sample performance of the proposed method, implying that our method is able to identify the covariates that affect the variance of the response. In addition, we apply the proposed method to analyze Boston house data, and find that this data set contains heteroscedasticity, which is caused by the variables of rm, dis, rad and ptratio.

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