Quantile regression: a nonparametric approach

Regression on any p-th quantile is considered through nonparametric modelling. The nonparametric technique used is moving parabolic fit which is known to be adaptative and to reduce bias in the usual mean regression. The quantile problem reduces to solving weighted linear regression in L1 norm at each x-point and the iteratively reweighted least squares algorithm is particularly suitable for this. Convergence of the IRLS algorithm is shown from a broad perspective. Implementation details are given and some illustrations are presented.