Backfitting and smooth backfitting in varying coefficient quantile regression

In this paper, we study ordinary backfitting and smooth backfitting as methods of fitting varying coefficient quantile models. We do this in a unified framework that accommodates various types of varying coefficient models. Our framework also covers the additive quantile model as a special case. Under a set of weak conditions, we derive the asymptotic distributions of the backfitting estimators. We also briefly report on the results of a simulation study.