On the Estimation of the Linear Relation when the Error Variances are known

The present article considers the problem of consistent estimation
in measurement error models. A linear relation with not necessarily
normally distributed measurement errors is considered. Three
possible estimators which are constructed as different combinations
of the estimators arising from direct and inverse regression are
considered. The efficiency properties of these three estimators are
derived and analyzed. The effect of non-normally distributed
measurement errors is analyzed. A Monte-Carlo experiment is
conducted to study the performance of these estimators in finite
samples and the effect of a non-normal distribution of the
measurement errors.