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多元非参数分位数回归常常是难于估计的, 为了降低维数同时保持非参数估计的灵活性, 人们常常用单指标的方法模拟响应变量的条件分位数. 本文主要研究单指标分位数回归的变量选择. 以最小化平均损失估计为基础, 我们通过最小化具有SCAD惩罚项的平均损失进行变量选择和参数估计. 在正则条件下, 得到了单指标分位数回归SCAD变量选择的Oracle性质, 给出了SCAD变量选择的计算方法, 并通过模拟研究说明了本文所提方法变量选择的样本性质.

Variable Selection of Single-Index Quantile Regression

Nonparametric quantile regression with multivariate covariates is a difficult estimation. To reduce the dimensionality while still retaining the flexibility of nonparametric model, the single-index regression is often used to model the conditional quantile of a response variable. In this paper, we focus on the variable selection aspect of single-index quantile regression. Based on the minimized average loss estimation (MALE), the variable selection is done by minimizing the average loss with SCAD penalty. Under some mild conditions, we demonstrate the oracle properties about SCAD variable section of single-index quantile regression. Furthermore, the algorithm of the variable selection of SCAD penalized quantile regression is given. Some simulations are done to illustrate the performance of the proposed methods.