Abstract: Although quantile regressions are widely employed for heterogeneous data, simultaneously selecting covariates that globally affect the response and estimating the coefficients is very challenging. We introduce a novel sparse composite quantile regression screening method for the analysis of ultrahigh-dimensional heterogeneous data. The proposed method enjoys the sure screening property, provides a consistent selection path, and yields consistent estimates of the coefficients simultaneously across a continuous range of quantile levels. An extended Bayesian information criterion is employed to select the "best" candidate from the path. Extensive simulation studies demonstrate the effectiveness of the proposed method, and an application to a gene expression data set is provided.

Key words and phrases: Quantile regression, sparsity, ultrahigh-dimensional data, variable screening.