Minimum distance partial linear regression model checking with Berkson measurement errors

We propose a class of tests for fitting a parametric model to the nonparametric part in partial linear regression models in the presence of Berkson measurement errors in the covariates. The proposed tests are based on certain minimized L2 distances between a semi-parametric regression function estimator and the parametric regression model being fitted. We establish asymptotic normality of the proposed test statistics and that of the corresponding minimum distance estimators under the fitted model. The consistency of the tests and their asymptotic power against certain local alternatives are also investigated. Simulation and comparison studies are included to evaluate the finite sample performance of the proposed tests.