Empirical Likelihood-based Dimension Reduction Inference for Linear Error-in-Responses Models with Validation Study

Abstract

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 Χ21 and the adjusted empirical loglikelihoods are proved to be asymptotically distributed as standard chi-squares, respectively. A simulation study is conducted to compare the proposed methods in terms of coverage accuracies and average lengths of the confidence intervals.