Some limit behaviors for the LS estimator in simple linear EV regression models

In the present paper, we study the simple linear errors in variables (EV) model: ηi=θ+βxi+εi,ξi=xi+δi, with i.i.d. errors (εi,δi),(1≤i≤n). The consistency and asymptotic normality for the LS estimators βˆn and θˆn of the unknown parameters β,θ are obtained, which weaken some known conditions and improve some known results. Finally, the large deviation principle for βˆn and θˆn are given under the assumptions that (εi,δi) possess normal distributions.