随机模型误差对参数估计的影响

Influence of Stochastic Model Error in Parameter Estimation

本文首先讨论了GLS关于协方差阵的稳键性问题,然后研究了定权误差对参数估值及其精度的影响规律,最后讨论了GLS估计的效率问题,并给出了两种评价效率的准则。

Considering adjustment model (A, σ_0~2Q) and (A, σ_0~2Q_e), this paper firstly proves if Q=Q_e+AD 1A^T +ZD_2Z^T , then. In case that Q and Q_e don't satisfy above condition, the influence of weight matrix error denoted by AP=P_e-P to the parameter estimator and its accuracy is investigated. Particulary for small △P, it is concluded that influence value is smaller than ·max(△p/p)and the covariance matrix of parameter has good robustness to the weight matrix of observations. Finally the relative efficienc y of two models is discussed. Especially, if P_e=I and max(p_1)/min(p_1)≤2.6, then the efficiency according to MSE criterion of equal weight to weighted adjustment will be at least 0.9.