分位数变系数模型基于核光滑的变量选择(英文)  

Variable Selection of Quantile Varying Coefficient Models Based on Kernel Smoothing

作　　者：赵为华[1] 张日权[2,3] 刘吉彩[2] 

机构地区：[1]南通大学理学院,南通226007 [2]华东师范大学金融与统计学院,上海200241 [3]山西大同大学数学系,大同037009

出　　处：《应用概率统计》2014年第5期537-560,共24页Chinese Journal of Applied Probability and Statistics

基　　金：supported in part by National Natural Science Foundation of China(11171112,11201190);Doctoral Fund of Ministry of Education of China(20130076110004);the Research Projects of Social Science and Humanity Fund of the Ministry of Education(14YJC910007);the Natural Science Project of Jiangsu Province Education Department(13KJB110024);the Natural Science Fund of Nantong University(13ZY001)

摘　　要：分位数变系数模型是一种稳健的非参数建模方法.使用变系数模型分析数据时,一个自然的问题是如何同时选择重要变量和从重要变量中识别常数效应变量.本文基于分位数方法研究具有稳健和有效性的估计和变量选择程序.利用局部光滑和自适应组变量选择方法,并对分位数损失函数施加双惩罚,我们获得了惩罚估计.通过BIC准则合适地选择调节参数,提出的变量选择方法具有oracle理论性质,并通过模拟研究和脂肪实例数据分析来说明新方法的有用性.数值结果表明,在不需要知道关于变量和误差分布的任何信息前提下,本文提出的方法能够识别不重要变量同时能区分出常数效应变量.Quantile varying coefficient model is one of the robust nonparametric modeling method. When one uses varying coefficient model to analyze data, a natural question is how to simultaneously select the relevant variables and separate the nonzero constant effect variables from nonzero varying effect variables. In this paper, we address the problem of both robustness and efficiency of estimation and variable selection procedure based on quantile regression. By combining the idea of the local kernel modeling and adaptive group Lasso method, we obtain penalized estimation through imposing double penalties on the quantile check function. With appropriate selection of tuning parameters by BIC criterion, the theoretical properties of the new variable selection procedure can be established. The finite sample performance of the new method is investigated through simulation studies and the analysis of body fat data. Numerical studies show that the new method can simultaneously identify unimportant variables and separate non-varying coefficient variables among important variables without any prior information about variables and irrespective of model error distribution.

关 键 词：变系数模型 分位数回归 变量选择 BIC准则 QKLASSO 核光滑. 

分 类 号：O212.7[理学—概率论与数理统计]