二阶可加混料模型的R-最优设计

阐明了依据线性回归模型参数联合估计的矩形置信区域所提出的一类具有崭新应用价值的最优设计准则R最优设计准则,介绍了该准则的等价定理和性质·同时针对(q-1)维正规单纯形上的二阶可加混料模型,证明了其参数估计的R最优设计柱点为单纯形的顶点和边界中心点;随着q的增加,边界中心点逐渐由一维过渡到二维中心点

R-Optimal Designs for an Additive Quadratic Mixture Model

A new class of optimality criteria i.e. R optimality criterion was described depending on a joint confidence rectangle for the parameter estimation. And its equivalence theorem and invariance property were given. This allows an easy calculation of optimal designs on many linearly transformed design spaces. An additive quadratic mixture model was chosen as an example for the R optimal designs. In the R optimal designs,support points are vertices of the simplex S q-1 and other support points shift gradually from barycentres of depth 1 to depth 2 as q increases.