ABSTRACT
The earliest computation of a median regression estimator is usually attributed to the Croatian Jesuit, Rudjer Boscovich. In 1760 Boscovich visited London and, as recounted by Stigler and Farebrother, posed the computation problem to Thomas Simpson. In Boscovich's version of the problem the mean residual was constrained to be zero, a requirement that conveniently reduces the problem to finding a weighted median. The algorithm of Barrodale and Roberts was the first to exploit the bounded variables dual form of the median regression problem. Edgeworth suggested an ingenious geometric strategy for the case of bivariate regression that anticipated later development of the simplex algorithm. Modification of the approach to compute quantile regression models other than the median is straightforward. A natural extension of the basic quantile regression problem that maintains its linear programming structure involves the imposition of additional linear inequality constraints on the model parameters.
