Local Linear Additive Quantile Regression

Abstract

Abstract. We consider non‐parametric additive quantile regression estimation by kernel‐weighted local linear fitting. The estimator is based on localizing the characterization of quantile regression as the minimizer of the appropriate ‘check function’. A backfitting algorithm and a heuristic rule for selecting the smoothing parameter are explored. We also study the estimation of average‐derivative quantile regression under the additive model. The techniques are illustrated by a simulated example and a real data set.