Simple linear functional Errors–In–Variables models with correlated errors

Abstract

This paper establishes a new estimator for simple linear measurement error models with correlated errors. Under a small-noise asymptotic regime and using perturbation theory, an unbiased estimator has been developed. The consistency and the asymptotic normality of the new estimator have been established and then validated by using synthetic data. Moreover, the confidence intervals of the slope have been revisited. Simulation results show that our estimator is certainly the most stable of existing methods and its performance exceeds that of other existing methods in terms of coverage and interval length.