带有测量误差的部分线性变系数模型的估计
Estimation of Partial Linear Variable Coefficient Model with Measurement Error
摘要: 一般在研究带有测量误差的部分线性变系数模型中，所研究的测量误差大多数存在于参数部分，且测量误差的类型主要为可加型测量误差。而此次主要研究测量误差在非参数部分的部分线性变系数模型，并且同时研究了部分线性变系数模型中非参数部分的变量带有的测量误差是可加型和非可加型两种情况。对于非参数部分的变量带有可加型测量误差的情况，利用纠偏的轮廓最小二乘估计方法对模型进行估计，而对于非参数部分的变量带有非可加型测量误差的情况，采用纠偏的一元化估计方法，对未知的常数系数以及函数系数进行估计得到估计的统计量，最后通过数值模拟分别验证了这两种估计方法的有效性。
Abstract: In the general study of partial linear variable coefficient models with measurement errors, most of the measurement errors studied exist in the parameter part, and the types of measurement errors are mainly additive measurement errors. This time, we mainly study the partial linear variable coefficient model with measurement error in the non-parametric part, and at the same time, the measurement errors of the non-parametric variables in the partial linear variable coefficient model are additive and non-additive. For nonparametric variables with additive measurement errors, the corrected contour least square estimation method is used to estimate the model; for the non-parametric part of the variables with non-additive measurement error, the unitary estimation method is used to correct the error, and the unknown constant coefficient and the function coefficient are estimated to get the estimated statistics. Finally, the effectiveness of the two estimation methods is verified by numerical simulation.
文章引用：郭佳佳, 叶瑶. 带有测量误差的部分线性变系数模型的估计[J]. 应用数学进展, 2021, 10(8): 2725-2732. https://doi.org/10.12677/AAM.2021.108283

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