带随机区组效应的反应曲面模型中处理效应估计的精度

Estimation and its Precision of Fixed Polynomial Effects of Response Surface Models with Random Block Effects

本文在混合设计模型中处理效应三类估计的基础上,研究了它们的精度;并证明了在区组设计正交条件下,区组内估计、经典LSE与联合估计(BLUE)有相同的方差,这一研究不仅改进了A.L.Khuri [3]的结果,而且为人们在混合试验设计中采用正交区组设计方案提供理论根据。

In this paper, we study the variances of used in mixed design model, and prove that, three estimators of treatment contrast, namely, intra-block estimator and least square estimator and intra-block inter-block combined estimator have the same variances, under the fact that the design block is orthogonal. The study develops A. L. Khuri's work[3] and presents an important theory basement for using orthogonal design in mixed blocks design.