Profile inference on partially linear varying-coefficient errors-in-variables models under restricted condition

In this paper, we investigate the estimation and testing problems of partially linear varying-coefficient errors-in-variables (EV) models under additional restricted condition. The restricted estimators of parametric and nonparametric components are established based on modified profile least-squares method, and their asymptotic properties are also studied under some regularity conditions. Moreover, the modified profile Lagrange multiplier test statistic is constructed under additional restricted condition. It is shown that the modified profile Lagrange multiplier test statistic is asymptotically distribution-free and follows a Chi-squared distribution under the null hypothesis. Some simulation studies are carried out to assess the performance of the proposed methods. A real dataset is analyzed for illustration.