Empirical likelihood for partially linear additive errors-in-variables models

This study investigates the empirical likelihood method for the partially linear additive models in which certain covariates are measured with additive errors. An empirical log-likelihood ratio for the parametric component is proposed based on the profile procedure, and a nonparametric version of the Wilk’s theorem is derived. Then, the confidence regions of the parametric component with asymptotically correct coverage probabilities are constructed by the obtained results. Furthermore, a simulation study is conducted to illustrate the performance of the proposed method.