Likelihood-based kernel estimation in semiparametric errors-in-covariables models with validation data

We present methods to handle error-in-variables models. Kernel-based likelihood score estimating equation methods are developed for estimating conditional density parameters. In particular, a semiparametric likelihood method is proposed for sufficiently using the information in the data. The asymptotic distribution theory is derived. Small sample simulations and a real data set are used to illustrate the proposed estimation methods.