LSE的稳健性

Robustness of the Least Squares Estimation

用不同于Zyskind的方法在LS估计的稳健性方面得到了一些新结论。首先,对设计矩阵列满秩,协方差矩阵非奇异的情形,给出了GLSE和LSE相等的两个充要条件和一个充分条件,揭示了GLSE和LSE相等与它们方差相等之间的关系,对设计矩阵的一般情形,给出了三个充分条件,较好地解决了这方面的问题。

On the robustness of LSE, using the methods other than Zyskind＇ s, some new results are gained. First, the case is discussed that the design matrix is row full order and covariance matrix is non-zero, get two s. n conditions and one sufficient condition in which GLSE is equivalent to LSE . The meaning point out that the variance of GLSE is the same as the variance of LSE . In common case, presenting three sufficient conditions , the problem is solved nicely.