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Distributional vs. Quantile Regression

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  • Roger Koenker

    (University of Illinois at Urbana-Champaign)

  • Samantha Leorato

    (University of Rome "Tor Vergata")

  • Franco Peracchi

    (University of Rome "Tor Vergata" and EIEF)

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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Bibliographic Info

Paper provided by Einaudi Institute for Economics and Finance (EIEF) in its series EIEF Working Papers Series with number 1329.

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Length: 42 pages
Date of creation: 2013
Date of revision: Dec 2013
Handle: RePEc:eie:wpaper:1329

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  1. Rothe, Christoph & Wied, Dominik, 2012. "Misspecification Testing in a Class of Conditional Distributional Models," IZA Discussion Papers 6364, Institute for the Study of Labor (IZA).
  2. Klein, Roger W & Spady, Richard H, 1993. "An Efficient Semiparametric Estimator for Binary Response Models," Econometrica, Econometric Society, vol. 61(2), pages 387-421, March.
  3. Victor Chernozhukov & Ivan Fernandez-Val & Alfred Galichon, 2010. "Quantile and Probability Curves without Crossing," Sciences Po publications info:hdl:2441/5rkqqmvrn4t, Sciences Po.
  4. Victor Chernozhukov & Ivan Fernandez-Val & Blaise Melly, 2009. "Inference on counterfactual distributions," CeMMAP working papers CWP09/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  5. Rothe, Christoph, 2011. "Partial Distributional Policy Effects," IZA Discussion Papers 6076, Institute for the Study of Labor (IZA).
  6. Holger Dette & Stanislav Volgushev, 2008. "Non-crossing non-parametric estimates of quantile curves," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(3), pages 609-627.
  7. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521608275, Fall.
  8. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  9. Joshua Angrist & Victor Chernozhukov & Iván Fernández-Val, 2006. "Quantile Regression under Misspecification, with an Application to the U.S. Wage Structure," Econometrica, Econometric Society, vol. 74(2), pages 539-563, 03.
  10. Foresi, S. & Paracchi, F., 1992. "The Conditional Distribution of Excess Returns: An Empirical Analysis," Working Papers 92-49, C.V. Starr Center for Applied Economics, New York University.
  11. Roger Koenker & Zhijie Xiao, 2002. "Inference on the Quantile Regression Process," Econometrica, Econometric Society, vol. 70(4), pages 1583-1612, July.
  12. Peracchi, Franco, 2002. "On estimating conditional quantiles and distribution functions," Computational Statistics & Data Analysis, Elsevier, vol. 38(4), pages 433-447, February.
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