The main features of the QUANTREG procedure are as follows:
supports single-level quantile regression analysis and quantile process regression analysis
offers simplex, interior point, and smoothing algorithms for estimation
supports the parametric simplex algorithm for quantile process regression that estimates the optimal quantile-level grid
supports the interior point and smoothing algorithms for fast quantile process regression that approximate the process by using a prespecified equally spaced quantile-level grid
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, likelihood ratio, and rank tests for the regression parameter estimates and the Wald test for heteroscedasticity
provides outlier and leverage-point diagnostics
enables parallel computing when multiple processors are available
provides rowwise or columnwise output data sets with multiple quantiles
provides regression quantile spline fits
produces fit plots, diagnostic plots, and quantile process plots by using ODS Graphics
supports conditional and marginal distribution estimation of the response random variable
The next section provides notation and a formal definition for quantile regression.