Consistent test of error-in-variables partially linear model with auxiliary variables

In this paper, we investigate the model checking problem of a partially linear model when some covariates are measured with error and some auxiliary variables are supplied. The often-used assumptions on the measurement error, such as a known error variance or a known distribution of the error variable, are not required. Also repeated measurements are not needed. Instead, a nonparametric calibration method is applied to deal with the measurement error. An estimating method for the null hypothetical model is proposed and the asymptotic properties of the proposed estimators are established. A testing method based on a residual-marked empirical process is then developed to check the null hypothetical partially linear model. The tests are shown to be consistent and can detect the alternative hypothesis close to the null hypothesis at the rate n−rn−r with 0≤r≤1/20≤r≤1/2. Simulation studies and real data analysis are conducted to examine the finite sample behavior of the proposed methods.