Some Limit Behaviors For LS Estimators In Simple Linear EV Regression Model With Dependent Measurements

In this paper, we consider the simple linear errors-in-variables (EV) regression mod-els: ηi=θ+βxi+εi, ξi=xi+δi,1≤i≤n, where θ, β, x1, x2,··· are unknownconstants (parameters),(ε1, δ1),(ε2, δ2),··· are errors and ξi, ηi, i=1,2,··· are observ-able. In chapter two, we obtain the asymptotic normality and strong consistency of theleast square (LS) estimators for the unknown parameters in the simple linear errors invariables (EV) model are established under the assumptions that the errors are stationarynegatively associated sequences; In chapter three, we obtain the asymptotic normality forthe least square (LS) estimators of the unknown parameters β and θ in the model are es-tablished under the assumptions that the errors are m-dependent, martingale diferences,-mixing, ρ-mixing and α-mixing.