协变量含误差下广义线性模型的SEE变量选择  

SEE Variable Selection for Generalized Linear Models with Error Prone Covariates

作　　者：赵培信[1] 杨宜平[2] 

机构地区：[1]河池学院数学与统计学院,广西宜州546300 [2]重庆工商大学数学与统计学院,重庆400067

出　　处：《应用数学》2015年第1期165-171,共7页Mathematica Applicata

基　　金：国家自然科学基金(11101119;11301569);广西中青年优秀骨干教师培养工程(GXQG012013093)资助

摘　　要：利用一些辅助信息作为工具变量并结合光滑门限估计方程(SEE)方法,针对协变量含有测量误差广义线性模型提出一个工具变量类型的变量选择方法.该方法可以在估计模型中非零回归系数的同时,剔除模型中不显著的协变量,从而达到变量选择的目的.另外,该变量选择过程不需要求解任何凸优化问题,从而具有较强的适应性并且在实际应用比较容易计算.理论证明该变量选择方法是相合的,并且对非零回归系数的估计达到了最优的参数收敛速度.数值模拟结果表明所提出的变量选择方法可以有效地消除测量误差对估计精度的影响,并且具有较好的有限样本性质.By using some auxiliary variables as instrumental variables and based on the smooth-threshold estimating equations （SEE） method, an instrumental variable based varia- ble selection procedure is proposed for generalized linear models with error prone covariates. The proposed procedure can automatically eliminate the irrelevant covariates hy setting the corresponding coefficients as zero,and simultaneously estimate the nonzero regression coeffi- cients by solving the smooth-threshold estimating equations. Furthermore, the proposed vari- able selection procedure avoids the convex optimization problem,and is flexible and easy to implement. This variable selection procedure is proved to be consistent, and the estimators of coefficient achieve the optimal convergence rate. Some simulation studies are carried out to assess the performance of the proposed variable selection method.

关 键 词：广义线性模型 光滑门限广义估计方程 协变量含误差 变量选择 

分 类 号：O212.7[理学—概率论与数理统计]