Semiparametric Estimation of Additive Quantile Regression Models by Two-Fold Penalty
提出一种基于样条逼近和SCAD双重惩罚的方法，用于加性分位数回归中的模型选择和半参数估计，能自动区分非线性、部分线性和线性成分，无需事先指定线性部分的协变量。
In this article, we propose a model selection and semiparametric estimation method for additive models in the context of quantile regression problems. In particular, we are interested in finding nonzero components as well as linear components in the conditional quantile function. Our approach is based on spline approximation for the components aided by two Smoothly Clipped Absolute Deviation (SCAD) penalty terms. The advantage of our approach is that one can automatically choose between general additive models, partially linear additive models, and linear models in a single estimation step. The most important contribution is that this is achieved without the need for specifying which covariates enter the linear part, solving one serious practical issue for models with partially linear additive structure. Simulation studies as well as a real dataset are used to illustrate our method.