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Dual regression

Authors: Richard Spady and Sami Stouli
Date: 16 January 2019
Type: cemmap Working Paper, CWP01/19
DOI: 10.1920/wp.cem.2019.0119

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 speci cation and estimation of a exible class of conditional distribution functions, and present asymptotic theory for the corresponding empirical dual regression process.

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Previous version:
Richard Spady and Sami Stouli January 2016, Dual regression, cemmap Working Paper, CWP04/16, Institute for Fiscal Studies

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