Statistical Papers

, Volume 59, Issue 2, pp 849–850 | Cite as

Roger Koenker, Victor Chernozhukov, Huming He and Limin Peng (2017): Handbook of Quantile Regression

Chapman & Hall/CRC, pp. xix–463, $119.95, ISBN: 978-1-4987-2528-6
  • David E. Giles
Book Review

The usual linear regression model considers the relationship between a group of explanatory variables, X, and a response variable, y, based on the conditional mean function E(y|X). Accordingly, this model gives us a rather narrow measure of the relationship, based on just one moment of the (conditional) distribution of y. It can be valuable to assess the relationship between y and X at different points in this conditional distribution. An obvious example would be use the median of the distribution, rather than the mean. It is well-known that this arises if we use an L1 norm, rather than an L2 norm, and “fit” the regression so as to minimize the sum of the absolute values of the residuals (giving us the Least Absolute Deviations (LAD) estimator for the regression coefficients) rather than the sum of their squared values.

Quantile regression (QR) provides us with a way of measuring the regression relationship at several points of the conditional distribution of ysimultaneously, and it...


  1. Koenker R (2005) Quantile regression. Cambridge University Press, CambridgeCrossRefzbMATHGoogle Scholar
  2. Koenker R, Bassett GW (1978) Regression quantiles. Econometrica 46:33–50MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of VictoriaVictoriaCanada

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