Galton, Edgeworth, Frisch, and prospects for quantile regression in econometrics

The work of three leading figures in the early history of econometrics is u sed to motivate some recent developments in the theory and application of q uantile regression. We stress not only the robustness advantages of this fo rm of semiparametric statistical method, but also the opportunity to recove r a more complete description of the statistical relationship between varia bles. A recent proposal for a more X-robust form of quantile regression bas ed on maximal depth ideas is described along with an interesting historical antecedent. Finally, the notorious computational burden of median regressi on, and quantile regression more generally, is addressed. It is argued that recent developments in interior point methods for linear programming toget her with some new preprocessing ideas make it possible to compute quantile regressions as quickly as least-squares regressions throughout the entire r ange of problem sizes encountered in econometrics. (C) 2000 Elsevier Scienc e S.A. All rights reserved.