Uniform Bahadur representation of the backfitting estimator for additive quantile models and its applications

This work is concerned with the Backfitting (BF) algorithm for the nonparametric additive quantile regression (AQR) model. We establish a strong uniform consistency rate for the Bahadur representation of the BF estimators, which includes the two stage estimator of [11] as a special case. These results are fundamental for statistical inference in AQR models and for applications that involve plugging such estimators into other functionals where some control over higher order terms is required. Two examples of applications are provided: one is on the root-n consistency of the parameter estimates for the partially linear AQR model, the other concerns structure recovery for the nonparametric AQR model.