在经济学、社会学、工程学、药物动力学和药效学等科学研究中，经常需要对同一试验单元的多项指标进行观测，而试验条件(如因子的水平等)可由试验人员选取。由此获得的数据不仅包含每个指标的信息，还包含各指标间的关联信息，能很好的反映出单个指标的变化和各指标间的联系。多响应线性模型是对这类数据进行建模和分析的重要统计工具之一。迄今为止，有多响应线性模型最优设计与稳健设计的研究方兴未艾，有关的理论与方法还不能满足实际需求，迫切需要深入与完善。.本项目旨在通过提供科学的试验设计方法，获得优质高效的数据，从而提高统计建模的精度和数据分析的可靠度。本项目借鉴并发展经典回归模型最优设计的理论与方法，研究设计的容许性、不变性和完备类；研究最优设计的几何刻画；研究波曼模型和球面模型的D-最优设计；研究多响应线性混合效应模型的最优设计。本项目的研究成果可直接应用于具有多个响应指标的科学试验的设计工作.

In an experiment often more than one dependent variable is observed for each observational unit. As typically observations are correlated within units, the data are properly described by a multiresponse linear model. Examples of this type of study are common in econometrics, social sciences, pharmacokinetics and pharmacodynamics. .This project aims at an efficient choice of the experimental conditions in order to optimize the performance of the statistical inference on the multiresponse linear model by the experimental data. The main topics of this project are as follows: (1) Study admissibility, invariance and complete classes; (2) Study geometric characterization of optimal designs; (3)Study the D-optimal designs for the Berman model and the spherical model; (4)Study the optimal designs for multiresponse linear models with mixed effects.