Data-driven model checking for errors-in-variables varying-coefficient models with replicate measurements

In this work, the adequacy check of errors-in-variables varying-coefficient models is investigated when replicate measurements are available. Estimation using the naive method that ignores measurement errors is biased. After the calibration of the estimators of the regression coefficient functions, we construct an empirical-process-based test statistic by the attenuation of corrected residuals. The asymptotic properties of the test statistic under the null hypothesis, global and various local alternatives are established. Simulation studies and real data analyses reveal that the proposed test performs satisfactorily.