Multiplicative regression models with distortion measurement errors
Multiplicative regression models with distortion measurement errors
复制标题
具有失真测量误差的乘法回归模型
DOI：
10.1007/s00362-018-1020-2
复制
发表时间：
2020-10-01
影响因子：
1.3
通讯作者：
Lu，Tao
中科院分区：
文献类型：
--
作者：
Zhang，Jun;Zhu，Junpeng;Lu，Tao
本文考虑了当响应变量和协变量都无法直接观察到，而是被常见可观察混杂变量的未知函数扭曲时，乘法线性回归模型的估计和变量选择。对响应变量进行对数变换后，我们提出了两种参数估计方法。一种是最小二乘估计器，第二种是与变化系数模型相关的基于矩的估计器。第三个是没有对数变换的最小乘积相对误差估计器。对于参数分量的假设检验，提出了原假设下的限制估计量和检验统计量。建立了估计量和检验统计量的渐近性质。建议采用引导程序来计算临界值。采用平滑修剪的绝对偏差罚分来选择相关变量。由此产生的惩罚估计量被证明是渐近正态的并且具有预言性质。仿真研究证明了所提出程序的性能，并分析了一个实际示例以说明其实际用途。
This paper considers estimation and variable selection for multiplicative linear regression models when neither the response variable nor the covariates can be directly observed, but are distorted by unknown functions of a commonly observable confounding variable. After taking logarithmic transformation on the response variable, we propose two estimation methods for the parameter. One is the least squares estimator, the second one is the moment-based estimator linked with varying coefficient models. The third one is the least product relative error estimator without logarithmic transformation. For the hypothesis testing of parametric components, restricted estimators under the null hypothesis and test statistics are proposed. The asymptotic properties for the estimators and test statistics are established. A bootstrap procedure is proposed to calculate critical values. A smoothly clipped absolute deviation penalty is employed to select the relevant variables. The resulting penalized estimators are shown to be asymptotically normal and have the oracle property. Simulation studies demonstrate the performance of the proposed procedure and a real example is analyzed to illustrate its practical usage.