Consistency for the LS estimator in the linear EV regression model with replicate observations

In this paper, we consider the following linear errors-in-variables regression model: ξij=xi+δij,ηij=yi+εij=θ+βxi+εij, with independent identically distributed errors (εij,δij),(j=1,2,…,ni;i=1,2,…). The strong and weak consistency for the LS estimators βˆ and θˆ of the unknown parameters β,θβ,θ in this model are obtained, which weaken some known conditions and improve some known results.