均方误差准则下多响应线性模型的最优设计

The Optimal Design for Multi-response Linear Models Based on a Mean Squared Error Ccriterion

WilliamJ.Welch（1983）给出了单响应线性模型均方误差准则下的最优试验设计。基于此结论,通过对多响应模型进行合理线性组合的方法将其转化为易于处理的单响应模型,由此给出均方误差准则下多响应模型最优设计的构造方法。解决了多响应线性模型预测的试验设计问题。

By William J.Welch（1983）a mean squared error criterion for optimal design of single-response linear model is given.Based on this result,the multi-response models are deal with by a linear combination to the responses for getting a manageable single-response model.Thus obtain the construction method of optimal design for multi-response linear models based on the mean squared error criterion.The optimal design problem for prediction of multi-response linear models is solved.