缺失数据下高维半参数变系数测量误差模型的惩罚经验似然  

Penalized Empirical Likelihood of High-Dimensional Semiparametric Varying Coefficient Errors-in-Variables Model Under Missing Data

作　　者：何帮强[1] 王龙 HE Bangqiang;WANG Long(School of Mathematics-Physics and Finance,Anhui Polytechnic University,Wuhu 241000)

机构地区：[1]安徽工程大学数理与金融学院,芜湖241000

出　　处：《系统科学与数学》2025年第2期603-612,共10页Journal of Systems Science and Mathematical Sciences

基　　金：国家社科基金一般项目(18BTJ034);国家自然科学基金面上项目(72271003)资助课题。

摘　　要：文章研究在响应变量缺失下高维半参数变系数测量误差模型的参数估计与变量选择问题.首先,基于逆概率加权方法分别构造了纠偏参数部分和非参数部分的估计,在适当的条件下证明纠偏的非参数估计具有渐近正态性.然后,构造了纠偏参数部分的经验对数似然比统计量,同时建议惩罚经验似然(PEL)进行变量选择,在适当的条件下证明了所提出的惩罚经验估计具有Oracle特征且在零假设下服从渐近卡方分布.Monte Carlo模拟研究表明,建议的估计在有限样本表现较好,最后给出一个实例研究.The article investigates the problem of parameter estimation and variable selection in high-dimensional semiparametric variable coefficient measurement error models with missing response variables.Firstly,based on the inverse probability weighting method,a random auxiliary vector for parameter partial correction and a nonparametric partial estimation function for correction are constructed.Under appropriate conditions,it is proven that the nonparametric estimation for correction follows asymptotic normality.Then,an empirical logarithmic likelihood ratio statistic for the correction parameter part is constructed and it is suggested that penalized empirical likelihood(PEL)be used to select variables.Under appropriate conditions,it is proven that the proposed penalized empirical estimate has oracle characteristics and obeys the asymptotic chi-square distribution under the null hypothesis.Monte Carlo simulation research suggests that the proposed estimation performs well in finite samples.Finally,a real data analysis is provided.

关 键 词：半参数变系数模型 测量误差 随机缺失 逆概率加权 惩罚经验似然 

分 类 号：O212.1[理学—概率论与数理统计]