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Distributional vs. Quantile Regression

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Abstract

Given a scalar random variable Y and a random vector X defined on the same probability space, the conditional distribution of Y given X can be represented by either the conditional distribution function or the conditional quantile function. To these equivalent representations correspond two alternative approaches to estimation. One approach, distributional regression (DR), is based on direct estimation of the conditional distribution function; the other approach, quantile regression (QR), is instead based on direct estimation of the conditional quantile function. Indirect estimates of the conditional quantile function and the conditional distribution function may then be obtained by inverting the direct estimates obtained from either approach. Despite the growing attention to the DR approach, and the vast literature on the QR approach, the link between the two approaches has not been explored in detail. The aim of this paper is to fill-in this gap by providing a better understanding of the relative performance of the two approaches, both asymptotically and in finite samples, under the linear location model and certain types of heteroskedastic location-scale models.

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  • Roger Koenker & Samantha Leorato & Franco Peracchi, 2013. "Distributional vs. Quantile Regression," CEIS Research Paper 300, Tor Vergata University, CEIS, revised 17 Dec 2013.
  • Handle: RePEc:rtv:ceisrp:300
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    4. Richey, Jeremiah & Rosburg, Alicia, 2016. "Understanding intergenerational economic mobility by decomposing joint distributions," MPRA Paper 72665, University Library of Munich, Germany.
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    10. Kolodziej, Ingo W.K. & García-Gómez, Pilar, 2017. "The causal effects of retirement on mental health: Looking beyond the mean effects," Ruhr Economic Papers 668, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
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    More about this item

    Keywords

    Quantile regression; distributional regression; functional Delta-method; asymptotic relative efficiency; linear location model; location-scale models.;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

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