A parametric hypothesis test for a global power law and local nonparametric trend model with multiplicative distortion measurement errors

We consider a parametric hypothesis test of the multiplicative distortion model with both a parametric global trend and a nonparametric local trend. In the model, neither the response variable nor the covariates can be directly observed, but are measured with multiplicative distortion measurement errors. Four calibration procedures with several estimation methods are used to construct the test statistics, namely, conditional mean calibration based test statistic, conditional absolute mean calibration based test statistic, conditional variance calibration based test statistic, and conditional absolute logarithmic calibration based test statistic. Asymptotic properties for these test statistics are established under the null hypothesis and alternative hypothesis. Monte Carlo simulation experiments are carried out to examine the performance of the proposed test statistics. A real example is analyzed to illustrate their practical usages.