Robust Quantile Regression

Abstract

Abstract Robust quantile regression is a collection of statistical procedures based on regression, autoregression and conditional quantiles and on regression and autoregression rank scores . These procedures can replace the classical estimation and testing procedures in the linear regression and autoregression models, based on least squares, in situations when we cannot guarantee that our observations follow the normal distribution. The character of these methods is nonparametric (i.e. they do not assume any specific probability distribution of the observations), and robust (with respect to outliers in the dependent variables). Moreover, the procedures based on the regression rank scores do not depend on an eventual nuisance regression, because the regression rank scores are invariant to the regression parameters, similarly as the ordinary ranks are invariant to the shift in location. Regression quantiles and regression rank scores are dual in the linear programming sense, but their relation also extends the duality of the quantiles (order statistics) and ranks from the location to the linear regression (autoregression) models.