Dual regression

Abstract

We propose dual regression as an alternative to quantile regression for the global estimation of conditional distribution functions. Dual regression provides the interpretational power of quantile regression while avoiding the need to repair intersecting conditional quantile surfaces. We introduce a mathematical programming characterization of conditional distribution functions which, in its simplest form, is the dual program of a simultaneous estimator for linear location-scale models, and use it to specify and estimate a flexible class of conditional distribution functions. We present asymptotic theory for the corresponding empirical dual regression process.