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

The work of three leading figures in the early history of econometrics is used to motivate some recent developments in the theory and application of quantile regression. We stress not only the robustness advantages of this form of semiparametric statistical method, but also the opportunity to recover a more complete description of the statistical relationship between variables. A recent proposal for a more X-robust form of quantile regression based on maximal depth ideas is described along with an interesting historical antecedent. Finally, the notorious computational burden of median regression, and quantile regression more generally, is addressed. It is argued that recent developments in interior point methods for linear programming together with some new preprocessing ideas make it possible to compute quantile regressions as quickly as least-squares regressions throughout the entire range of problem sizes encountered in econometrics.