This paper considers the partially linear mixed-effect model relating a response Y to predictors $(X,Z,T)$ with mean function $X^{\mathrm{T}}\text{β}+Z^{\mathrm{T}}b+g\left(T\right)$ which is a combination of the linear mixed-effect model and the nonparametric smooth function. The proposed model contains an additive measurement error in X. Taavoni and Arashi (Kernel estimation in semiparametric mixed-effect longitudinal modelling. Statist Papers. 2019. Available from: https://doi.org/10.1007/s00362-019-01125-8.) approximated the nonparametric function by the profile kernel method, and made use of the weighted least squares to estimate the regression coefficients when measurement error was ignored. We derive a simple modification of their estimators by correction for attenuation stems from measurement error and demonstrate that the linear parts estimator is asymptotically normal.

本文考虑了将响应Y与预测变量相关的部分线性混合效应模型$（X，ž，Ť）$ 具有平均功能 $X^{\mathrm{Ť}}\text{β}+{ž}^{\mathrm{Ť}}b+G（Ť）$它是线性混合效应模型和非参数平滑函数的组合。所提出的模型包含X的附加测量误差。Taavoni和Arashi（半参数混合效应纵向建模中的核估计。统计数据.2019。可从以下网址获得：https：//doi.org/10.1007/s00362-019-01125-8。）通过轮廓核方法近似了非参数函数。 ，并且在忽略测量误差时利用加权最小二乘估计回归系数。我们通过校正源自测量误差的衰减来推导其估计量的简单修改，并证明线性部分估计量是渐近正态的。