响应变量缺失的半参数 EV 模型估计的渐近正态性  

Asymptotic Properties for Estimators in Semi-Parametric Error-in-Variables Model with Missing Responses

作　　者：杨雪 张晶晶 胡婷婷 

机构地区：[1]上海理工大学理学院,上海

出　　处：《应用数学进展》2022年第7期4335-4354,共20页Advances in Applied Mathematics

摘　　要：本文重点研究半参数模型中估计量的性质,根据实际情况特别考虑了缺失数据和测量误差的影响。 缺失数据采用三种不同的方法处理:直接删除法、插值填补法和回归插值法。同时,得到了斜率参数和非参数变量的相应估计量。在合适的条件下,我们深入研究了这些估计量的渐近正态性,为未知参数和函数的置信区间的构建提供了基础。此外,在不同的样本量和缺失概率下也对理论结果进行了数值模拟,其结果与理论结果一致。This paper, concentrating on the properties of estimators in semi-parametric models, particularly considers the effects of missing data and measurement errors according to the actual situation. The missing data are processed by three different methods: di- rect deletion method, imputation(interpolation fill) method, and regression surrogate method. Also, the corresponding estimators of slope parameter and non-parameter variable are obtained. Under suitable conditions, the asymptotic normality of these estimators is studied thoroughly, which provides the basis for the construction of con- fidence intervals for unknown parameters and functions. In addition, different sample sizes and missing probabilities were set for simulation, whose results are consistent with the theoretical results.

关 键 词：半参数模型 测量误差 响应变量缺失 渐近正态性 

分 类 号：O212[理学—概率论与数理统计]