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

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 

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

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2005年第48卷第7期

页      面：915-928页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

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

主　　题：EV regression model unbiased estimate identiflability. 

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.