线性模型的最小二乘估计与马尔科夫估计

Least Square Estimation and Markov Estimation for Linear Model

通过引入马尔科夫估计的概念，指出线性模型Ｙ＝ＸＡ＋Ｗ中，当Ｗ非ｉ．ｉ．ｄ．时最小二乘估计失去最优性。马尔可夫估计是在Ｗ的协方差阵Ｇ已知时的最优估计。并给出Ｗ的协方差阵未知时，最优估计的求法。实际上是最小二来估计在非ｉ．ｉ．ｄ．情况的推广。

By introducing Markov estimation, we indicate least square estimate loses the optimum in the linear model Y=AN + W when W is non-i. i. d.. Markov estimation is the optimum estimation with given covariance matrix G of W We present a method to calculate the optimum estimation when the covariance matrix W is not given. This algorithm is an extension of least square estimation in non-i. i. d.