Weighted bias-corrected restricted statistical inference for heteroscedastic semiparametric varying-coefficient errors-in-variables model

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.