Semiparametric linear transformation model with differential measurement error and validation sampling

For the semiparametric linear transformation model with covariate measurement error and validation sampling, we propose an estimation method to estimate the covariate coefficient. The method updates the validation set based estimator to get a more efficient estimator using the data information available on the whole cohort. It can be used to deal with both differential and nondifferential measurement errors. Consistency and asymptotic normality are established for the proposed estimator and a closed form formula is derived for the limiting variance–covariance matrix. Simulation studies and a real data analysis are used to illustrate the performances of the proposed method.