| Existence of unbiased estimate of regression parameters in simple linear EV models |
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| 作者姓名： | LIU Jixue & CHEN Xiru |
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| 作者单位： | LIU Jixue & CHEN Xiru 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 |
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| 摘 要： | 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 a and βare not identifiable without some restriction imposed on the parameters. This paper discusses the problem of existence of unbiased estimate for a and βunder 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 a and βexist, and the form of the MVUE of a and βare also given.
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| 收稿时间： | 22 March 2004 |
Existence of unbiased estimate of regression parameters in simple linear EV models |
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| LIU Jixue & CHEN Xiru.Existence of unbiased estimate of regression parameters in simple linear EV models[J].Science in China(Mathematics),2005,48(7):915-928. |
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| Authors: | Liu Jixue CHEN Xiru |
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| Institution: | 1. 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
2. Department of Mathematics, Graduate School of Chinese Academy of Sciences, Beijing 100049, China |
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| Abstract: | It is well known that for one-dimensional normal EV regression modelX = x + u,Y = α + βx +e, wherex,u,e are mutually independent normal variables andEu =Ee = 0, the regression parameters α and β 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 and β exist, and the form of the MVUE of α and β are also given. |
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| Keywords: | EV regression model unbiased estimate identiflability |
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