Empirical likelihood-based dimension reduction inference for linear error-in-responses models with validation study

In this paper, linear errors-in-response models are considered in the presence of validation data on the responses. A semiparametric dimension reduction technique is employed to define an estimator of β with asymptotic normality, the estimated empirical loglikelihoods and the adjusted empirical loglikelihoods for the vector of regression coefficients and linear combinations of the regression coefficients, respectively. The estimated empirical log-likelihoods are shown to be asymptotically distributed as weighted sums of independent X ² ₁ and the adjusted empirical loglikelihoods are proved to be asymptotically distributed as standard chi-squares, respectively.