双侧截断回归模型的变量选择  

Variable selection in doubly truncated regression models

作　　者：郑明[1] 林婵娟 郁文 Ming Zheng;Chanjuan Lin;Wen Yu

机构地区：[1]复旦大学管理学院统计与数据科学系,上海200433

出　　处：《中国科学：数学》2022年第12期1433-1448,共16页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11771095和12071088)资助项目。

摘　　要：在回归分析中,当因变量存在双侧截断时,已有的统计方法会使得回归模型的系数估计与变量选择产生偏差.本文提出一种适用于双侧截断回归模型的系数估计与变量选择方法,且该方法允许回归模型中自变量的个数随着样本量增大并趋于无穷而趋于无穷.该方法的主要思想是,提出一种Mann-Whitney型的损失函数来进行纠偏,随后加入自适应最小绝对收缩和选择算子(least absolute shrinkage and selection operator,LASSO)惩罚项来进行变量选择.本文同时设计一种迭代算法来实现损失函数的优化;且证明了所提出估计量的相合性与渐近正态性,还给出所提出变量选择方法的神谕性(oracle property).本文通过随机模拟展示所提出方法在有限样本量下的表现,并使用所提出方法分析一个天文学领域的实际数据集.Doubly truncated data arise in many areas such as astronomy,econometrics,and medical studies.For the regression analysis with doubly truncated response variables,the existence of double truncation may bring bias for the estimation as well as affect the variable selection.We propose a simultaneous estimation and variable selection procedure for the doubly truncated regression,allowing a diverging number of regression parameters.To remove the bias introduced by the double truncation,a Mann-Whitney-type loss function is used.The adaptive LASSO(least absolute shrinkage and selection operator)penalty is added to the loss function to achieve simultaneous estimation and variable selection.An iterative algorithm is designed to optimize the resulting objective function.We establish the consistency and the asymptotic normality of the proposed estimator.The oracle property of the proposed selection procedure is also obtained.Some simulation studies are conducted to show the finite sample performance of the proposed approach.We also apply the method to analyze a real astronomical data set.

关 键 词：双侧截断 变量选择 维数发散 自适应LASSO 最小绝对离差 神谕性 

分 类 号：O212.1[理学—概率论与数理统计]