Existence of unbiased estimate of regression parameters in simple linear EV models

It is well known that for one-dimensional normal EV regression model X = x +u, Y= α+βx+e, where x, u, e are mutually independent normal variables and Eu = Ee= 0,the regression parameters α andβ are not identifiable without some restriction imposed on the parameters. This paper discusses the problem of existence of unbiased estimate for α and β under some restrictions commonly used in practice. It is proved that the unbiased estimate does not exist under many such restrictions. We also point out one important case in which the unbiased estimates of α andβ exist, and the form of the MVUE of α and β are also given.

作 者： Liu Jixue CHEN Xiru   作者單位： Liu Jixue(Department of Statistics and Finance, University of Science and Technology of China, Hefei 230026,China;Department of Mathematics, Graduate School of Chinese Academy of Sciences, Beijing 100049, China)

CHEN Xiru(Department of Mathematics, Graduate School of Chinese Academy of Sciences, Beijing 100049, China) 

刊 名： 中國科學A輯（英文版）  SCI 英文刊名： SCIENCE IN CHINA (MATHEMATICS)  年，卷(期)： 2005 48(7)  分類號： P3  關鍵詞： EV regression model   unbiased estimate   identifiability  

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