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 mea-surement 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 ana-lyzed. 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. 1 In a linear measurement error model, the parameters can be estimated consistently only when some additional information besides the data set is available. There are various ways such additional information can be employed; e.g.; Cheng an