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: η_i=θ+βx_i+ε_i,ξ_i=x_i+δ_i,1≤i≤n, where θ,β,x₁,x₂,… are unknown constants (parameters), (ε₁,δ₁),(ε₂,δ₂),… are errors and ξ_i,η_i,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, ?-mixing, ρ-mixing and α-mixing.