Central limit theorems for LS estimators in the EV regression model with dependent measurements

In this paper, we consider the simple linear errors-in-variables (EV) regression models: ηi=θ+βxi+εi,ξi=xi+δi,1≤i≤n, where θ,β,x1,x2,… are unknown constants (parameters), (ε1,δ1),(ε2,δ2),… are errors and ξi,ηi,i=1,2,… are observable. The asymptotic normality for the least square (LS) estimators of the unknown parameters β and θ in the model are established under the assumptions that the errors are m-dependent, martingale differences, ϕ-mixing, ρ-mixing and α-mixing.