部分线性单指标模型的复合分位数回归及变量选择

本文提出复合最小化平均分位数损失估计方法 (composite minimizing average check loss estimation,CMACLE)用于实现部分线性单指标模型(partial linear single-index models,PLSIM)的复合分位数回归(composite quantile regression,CQR).首先基于高维核函数构造参数部分的复合分位数回归意义下的相合估计,在此相合估计的基础上,通过采用指标核函数进一步得到参数和非参数函数的可达最优收敛速度的估计,并建立所得估计的渐近正态性,比较PLSIM的CQR估计和最小平均方差估计(MAVE)的相对渐近效率.进一步地,本文提出CQR框架下PLSIM的变量选择方法,证明所提变量选择方法的oracle性质.随机模拟和实例分析验证了所提方法在有限样本时的表现,证实了所提方法的优良性.

Composite quantile regression and variable selection of the partial linear single-index models

Abstract In this paper, we propose a composite minimizing average check loss estimation （CMACLE） method for the composite quantile regression （CQR） of the partial linear single-index model （PLSIM） by local linear method. Based on constructive approach, the estimators by CMACLE are able to achieve the best convergence rate. The asymptotical normalities of the estimators are also derived. Meanwhile, the asymptotic efficiency of the CQR estimation relative to the mean regression are investigated. Further more, we propose a variable selection method for the CQR of PLSIM by combining the CMACLE procedure with the adaptive LASSO penalized method. The oracle properties of the proposed variable selection method are also established. Simulations with various non-normal errors and a real data analysis are conducted to assess the finite sample property of the proposed estimation and variable selection methods.