典型有偏估计方法均方误差极小值一致性分析

The Minimum Consistency Analysis of the Mean Squares Error for Typical Biased Estimators

针对高斯-马尔科夫定理只能保证最小二乘估计在线性无偏估计类中具有最小方差,和目前有偏估计对最小二乘估计的改善程度研究甚少的现状,提出研究典型有偏估计方法的均方误差极小值的一致性。结果表明:尽管不同有偏估计方法具有不同的结构形式,但是这些有偏估计方法对最小二乘估计方差的改善程度是相同的,即均方误差的极小值总是相等的。实例分析结果也表明:典型有偏估计方法的均方误差极小值是一致的。

Gauss-Markov theorem can only guarantee that the least squares estimation has the minimum variance in the linear unbiased estimation class.Considering poor study on making use of biased estimation to improve the least squares estimation,investigating the consistency of the minimum mean square error of the typical biased estimation methods was proposed.The results show that,different biased estimation methods have different structural forms and these biased estimation methods can improve the least squares estimation variance to the same degree.That is,the minimum value of the mean square error is always equal.A case analysis indicates that the minimum mean square error of the typical biased estimation method is consistent.