误差的协方差阵不正确时的Gauss─Markov估计  

The Gauss─Markov estimation of error with an incorrect covariance matrix

作　　者：张帼奋[1] 林春土[1] 

机构地区：[1]浙江大学数学系

出　　处：《浙江大学学报（自然科学版）》1996年第5期510-516,共7页

基　　金：省自然科学基金

摘　　要：考虑线性模型ｙ＝Ｘβ＋ε，其中Ｅ（ε）＝０，Ｄ（ε）＝Ｖ０，记为（ｙ，Ｘβ，Ｖ０），当Ｖ０被弄错当成Ｖ１时，记为（ｙ，Ｘβ，Ｖ１）．对于两个问题，一是Ｘβ在（ｙ，Ｘβ，Ｖ１）下的ＢＬＵＥ也是Ｘβ在（ｙ，Ｘβ，Ｖ０）下的ＢＬＵＥ的充要条件是什么，二是Ｘβ在（ｙ，Ｘβ，Ｖ０）和（ｙ，Ｘβ，Ｖ１）下有公共的ＢＬＵＥ的充要条件是什么，本文在已有结论上又给出了几条新的等价的充要条件，并将众多等价的充要条件给出统一的证明．onsider linear model y= Xβ + ε,where E(ε) = 0,D(ε) = V0,written as(y,Xβ,V0)When V0 is mistaken to be V1,written as (y,Xε,V1 ),on the following two questions,i. e.,first,what is the necessary and sufficient condition for the BLUE of Xβ under (y,Xβ,V1 ) tobe at the same time the BLUE of Xβ under (y,Xβ,V0),and second,what is the necessary and sufficient condition for Xβ under (y,Xβ,V0) and (y,Xβ,V1) having a common BLUE,this paper gives,on the basis of existing conclusions,several new equal value necessary and sufficient conditions,and gives a unified version to prove the necessary and sufficient conditions of the various equal value.

关 键 词：线性模型 BLUE 参数估计 G-M估计 误差 

分 类 号：O212.1[理学—概率论与数理统计]