In this paper, we consider statistical inference for a heteroscedastic semiparametric varying-coefficient partially linear model with measurement errors in the nonparametric component when exact linear restriction on the parametric component is assumed to hold. Two types of weighted bias-corrected restricted estimators of the parametric and nonparametric components are proposed based on a bias-corrected estimator of the variance function, which is proposed by the nonparametric kernel estimation. The asymptotic properties of the resulting estimators are established under some regularity conditions. Moreover, we further proposed a weighted bias-corrected profile Lagrange multiplier test statistic to check whether the linear restriction of the model is valid. Finally, some simulation studies and a real data example are conducted to assess the performance of our proposed estimators and the testing procedure in finite samples.

在本文中，当假定对参数分量具有精确的线性约束时，我们考虑具有非测量分量误差的异方差半参数变系数部分线性模型的统计推断。基于由非参数核估计提出的方差函数的偏差校正估计量，提出了参数分量和非参数分量的两种加权偏差校正限制估计量。在某些规则性条件下建立了所得估计量的渐近性质。此外，我们还提出了加权偏差校正轮廓拉格朗日乘数检验统计量，以检查模型的线性约束是否有效。最后，