Dual Regression

TL;DR

This paper introduces dual regression as a new method for estimating conditional distribution functions, offering interpretability and avoiding issues common in quantile regression.

Contribution

It presents a novel dual regression approach that provides a mathematical programming characterization of conditional distributions, improving upon quantile regression.

Findings

Provides a new dual regression method for conditional distribution estimation.

Develops asymptotic theory for the empirical dual regression process.

Offers a flexible class of models with theoretical guarantees.

Abstract

We propose dual regression as an alternative to the quantile regression process for the global estimation of conditional distribution functions under minimal assumptions. Dual regression provides all the interpretational power of the quantile regression process while avoiding the need for repairing the intersecting conditional quantile surfaces that quantile regression often produces in practice. Our approach introduces 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. We apply our general characterization to the specification and estimation of a flexible class of conditional distribution functions, and present asymptotic theory for the corresponding empirical dual regression process.