Minimax Regression Quantiles

A new quantile regression estimator is developed and it is shown to be consistent and asymptotically normal. The estimator is based on estimating functions to which one can obtain consistent roots by finding the minimax of a certain deviance function. This function is conveniently constructed to have certain properties and relations to the estimating functions. Its asymptotic properties are equivalent to those of the classic quantile regression estimator. However, it is a different and therefore new estimator which allows for both linear- and nonlinear model specifications. The potential of the minimax framework, and extensions of the basic estimator derived here, could have important implications; the obvious example being non-diagonal weighting of observations to account for e.g. within-panel correlation. A simple algorithm for computing the estimates is proposed