Regression with errors in variables: estimators based on third order moments

In this paper consistent and, in a well–defined sense, optimal moment–estimators of the regression coefficient in a simple regression model with errors in variables are derived. The asymptotic variance and other asymptotic properties of these estimators are given. As is known for a long time, serious estimation problems exist in this model. There are two ways out of this problem: using either additional assumptions or additional information in the data. A lot of attention has been paid to the use of additional assumptions. However, quite often this leads to rather unrealistic models. In this paper we use additional information in the data. That means here that, besides first and second order moments, third order moments are formulated as functions of the model parameters. Besides theoretical derivations a small study with generated data is discussed. This study shows that for samples larger than 50 the estimates we consider behave nicely.