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 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.
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.
基金
This work was supported by the National Natural Science Foundation of China(Grant No.10231030).
