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
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。
Abstract: 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.
文章引用：杨雪, 张晶晶, 胡婷婷. 响应变量缺失的半参数 EV 模型估计的渐近正态性[J]. 应用数学进展, 2022, 11(7): 4335-4354. https://doi.org/10.12677/AAM.2022.117460

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