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

Science China Mathematics 2005年第7期48卷 915-928页

作者： 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 1. Department of Statistics and Finance University of Science and Technology of China 230026 Hefei China 2. Department of Mathematics Graduate School of Chinese Academy of Sciences 100049 Beijing China

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 β are not identifiable without some restriction imposed on the parameters. This paper discusses the problem of existence of unbiased estimate for a 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 a and β exist, and the form of the MVUE of a and β are also given.

关键词： EV regression model unbiased estimate identiflability.

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Theorem of Logarithm Expectation and Its Application to Prove Sample Correlation Coefficient as unbiased estimate

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Journal of Mathematics and System Science 2014年第9期4卷 605-608页

作者： Loc Nguyen Vietnam Institute of Mathematics Vietnam

In statistical theory, a statistic that is function of sample observations is used to estimate distribution parameter. This statistic is called unbiased estimate if its expectation is equal to theoretical parameter. Proving whether or not a statistic is unbiased estimate is very important but this proof may require a lot of efforts when statistic is complicated function. Therefore, this research facilitates this proof by proposing a theorem which states that the expectation of variable x 〉 0 is u if and only if the limit of logarithm expectation of x approaches logarithm of u. In order to make clear of this theorem, the research gives an example of proving correlation coefficient as unbiased estimate by taking advantages of this theorem.

关键词： Logarithm expectation correlation coefficient unbiased estimate

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