关于混合设计模型处理效应估计的进一步讨论

Further Discussion on the Estimators of Treatment Effects in Mixed Model

１９９２年Ｋｈｕｒｉ．Ａ．Ｌ提出在区组设计正交条件下，混合设计模型中参数向量β（不含β＿０）的区组内估计与联合估计是一致的；本文则研究了混合设计模型中位置参数β＿０的三种估计，并证明了在区组设计正交条件下β＿０的区组内估计β＿０＊、经典ＬＳＥβ＿０，与联合估计β是一致的．这一工作将Ｋｈｕｒｉ．Ａ．Ｌ的结果推广到处理效应的全部待估参向量τ＝（β＿０，β＇）＇在区组设计正交条件下都是一致的，对人们在混合设计中采用正交区组方案提供了更完整的理论依据。

In l992,Khuri A.L.has proved that the intra-block estimator and combinedestimators of Vector parameter β(ignoresβ_0)in mixed model are identically under the factthat the design blocks is orthogonally.In this paper,the main emphasis of the proposeddiscussion is three eatimators for the location parameterβ_0 in the Model.It is proved,thatβ_0*(the intra一block estimator),β(the ordinarg LSE)and β(the combined estimator)areidentically in orthogonally block design. The work extends Khuri’s resuIts to all parame-ter τ=(β_0,β')';and presents the reasonable basement for mixed block design using orthog-onally design.