CAJ | 학술논문

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.
천명료의거선성회귀모형삼수연합고계적구형치신구역소제출적일류구유참신응용개치적최우설계준칙R-최우설계준칙,개소료해준칙적등개정리화성질.동시침대(q-1)유정규단순형상적이계가가혼료모형,증명료기삼수고계적R-최우설계주점위단순형적정점화변계중심점;수착q적증가,변계중심점축점유일유과도도이유중심점.
A new class of optimality criteria i.e. R-optimality criterionwas 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 Sq-1 and other support points shift gradually from barycentres of depth 1 to depth 2 as q increases.