以减小均方误差为目标的估计

Estimation Aiming at Reducing Mean Squared Errors

文章分析了病态问题的特点,提出此时以最小方差为估计准则的LS估计常不能获得稳定的解,另一比较奏效的估计准则是均方误差最小。提出了均方误差意义下的最优线性估计,将其与正则化估计对照,获得了对正则化估计更加深入的认识,而正则化估计在均方误差意义下是优于最小二乘估计的。提出了基于正则化估计的单位权方差的无偏估计公式。

In this paper the character of ill-posed problem is analyzed in detail, the estimation criterion of the least variance is sometimes no longer a proper criterion, as the least square estimation is rather unstable. Another effective criterion is the least mean squared errors. The best linear estimation in the sense of the least mean squared errors is put forword. The comparison between it and regularization has been made, a deep recognizion to regularization is obtained, and the regularization is superior to the least square estimation in the sense of the least mean squared errors. The unbiased estimation formula of unit weight mean square error in the regularization solution is derived.