Dual Regression

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...

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Bibliographic Details
Published in:arXiv.org 2018-09
Main Authors: Spady, Richard, Stouli, Sami
Format: Article
Language:English
Subjects:
Distribution functions
Economic models
Maintenance
Mathematical programming
Regression
Regression analysis
Scale models
Online Access:Get full text
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Summary: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.
ISSN:2331-8422