The main features of the QUANTREG procedure are as follows:

• offers simplex, interior point, and smoothing algorithms for estimation

• provides sparsity, rank, and resampling methods for confidence intervals

• provides asymptotic and bootstrap methods for covariance and correlation matrices of the estimated parameters

• provides the Wald and likelihood ratio tests for the regression parameter estimates

• provides outlier and leverage-point diagnostics

• enables parallel computing when multiple processors are available

• provides row-wise or column-wise output data sets with multiple quantiles

• provides regression quantile spline fits

• produces fit plots, diagnostic plots, and quantile process plots by using ODS Graphics

The next section provides notation and a formal definition for quantile regression.