Dual regression

Research, Article, Preprint English OPEN
Spady, Richard ; Stouli, Sami (2018)
  • Publisher: London: Centre for Microdata Methods and Practice (cemmap)
  • Related identifiers: doi: 10.1093/biomet/asx074
  • Subject: Monotonicity | Duality | Mathematical programming | Statistics - Applications | Conditional distribution | Economics - Econometrics | Statistics - Methodology | Quantile regression | Convex approximation | Method of moments
    • ddc: ddc:330
    arxiv: Statistics::Methodology | Statistics::Computation | Statistics::Theory

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.
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