Gauss—Markov模型的几乎无偏估计

Almost Unbiased Estimation in Gauss -Markov Model

现有的有偏估计在减小均方误差时，都忽视了对估计偏差的限制，致使偏差都比较大。本文提出Gauss—Markov模型的几乎无偏估计，着重减小有偏估计的偏差，使之几乎接近无偏。给出了岭估计、岭-压缩组合估计、岭-主成分组合估计对应的几乎无偏估计，讨论了这些几乎无偏估计的一些优良性质，提出了几乎无偏估计中偏参数的选择准则和方法。最后给出了一个算例，显示了几乎无偏估计的优越性。

The current biased estimators always put emphasis on reduction of MSE, but ignore the bias control. This paper puts forward almost unbiased estimators based on Gauss - Markov model aiming at decreasing of bias and presents three typical almost unbiased estimators of OR estimator, CRS estimator and CRPC estimator. Then,it proves some of their good properties, and gives some criterions and methods for choosing the partial parameters. Finally, some examples have proved the superiority of the almost unbiased estimators.