Some limit behaviors for the LS estimators in errors-in-variables regression model

Abstract

There has been a continuing interest among statisticians in the problem of regression models wherein the independent variables are measured with error and there is considerable literature on the subject. In the following report, we discuss the errors-in-variables regression model: yi = β0 + β1xi + β2zi + ϵi,Xi = xi + ui,Zi = zi + vi with i.i.d. errors (ϵi, ui, vi), for i = 1, 2, ..., n and find the least square estimators for the parameters of interest. Both weak and strong consistency for the least square estimators βˆ0, βˆ1, and βˆ2 of the unknown parameters β0, β1, and β2 are obtained. Moreover, under regularity conditions, the asymptotic normalities of the estimators are reported.