SIMEX Estimation of Partially Linear Multiplicative Regression Model with Mismeasured Covariates

In many practical applications, such as the studies of financial and biomedical data, the response variable usually is positive, and the commonly used criteria are based on absolute errors, which is not desirable. Rather, the relative errors are more of concern. We consider statistical inference for a partially linear multiplicative regression model when covariates in the linear part are measured with error. The simulation-extrapolation (SIMEX) estimators of parameters of interest are proposed based on the least product relative error criterion and B-spline approximation, where two kinds of relative errors are both introduced and the symmetry emerges in the loss function. Extensive simulation studies are conducted and the results show that the proposed method can effectively eliminate the bias caused by the measurement errors. Under some mild conditions, the asymptotic normality of the proposed estimator is established. Finally, a real example is analyzed to illustrate the practical use of our proposed method.