高斯—马尔可夫定理研究新进展

New Research Progress on Gauss-Markov Theorem

高斯—马尔可夫定理被计量经济学家Hansen推广为“现代”高斯—马尔可夫定理,该定理在不增加任何额外条件的情况下去掉了高斯—马尔可夫定理对估计量的“线性”限制,认为所有线性或非线性估计中,最小二乘估计量是最优无偏估计量。针对Hansen的“现代”高斯—马尔可夫定理创新性提出了三点商榷和两个值得进一步探讨的问题。认为以下两个问题存在进一步探讨的必要性:(1)是否存在非线性无偏估计量的集合;(2)高斯—马尔可夫定理对估计量的“线性”限制是否可以放弃。

Gauss-Markov Theorem has been extended to"modern"Gauss-Markov Theorem by the econometrist Hansen,which removes the"linear"limitation of Gauss-Markov Theorem on estimators without adding any additional conditions,and believes that the least square estimator is the optimal unbiased estimator in all linear or nonlinear estimates.In view of Hansen's"modern"Gauss Markov theorem,this paper puts forward for the first time three points for discussion and two problems worthy of further exploration.This paper considers it necessary to explore the following two problems:(1)Whether there is a set of nonlinear unbiased estimators;(2)Whether the"linear"limitation of Gauss-Markov Theorem on estimators can be abandoned.