Nonparametric Estimation of an Additive Quantile Regression Model
本文提出一种非参数加性分位数回归模型的估计方法，该估计量渐近正态且收敛速度与协变量维数无关，避免了维数灾难，并具有oracle性质，适用于高维数据。
This article is concerned with estimating the additive components of a nonparametric additive quantile regression model. We develop an estimator that is asymptotically normally distributed with a rate of convergence in probability of n−r/(2r+1) when the additive components are r-times continuously differentiable for some r ≥ 2. This result holds regardless of the dimension of the covariates, and thus the new estimator has no curse of dimensionality. In addition, the estimator has an oracle property and is easily extended to a generalized additive quantile regression model with a link function. The numerical performance and usefulness of the estimator are illustrated by Monte Carlo experiments and an empirical example.