Asymptotic Normality of Least-Square Estimator for System Parameters and its Application

Abstract:

      In this paper we prove the asymptotic normality of leastsquare estimator for system parameters using the central limit theorem for martingales. And we obtaine the criterion that distinguishes the two groups of data come from the same dynamic system or not. We prove that F=(S₃(N₁) N₂-4n)/(S₁2n) has an asymptotic F-distribution with 2n and N₁ N₂ - 4n degrees of freedom.