随机系数回归模型的最优设计.pdf

上海师范大学硕士学位论文随机系数回归模型的最优设计姓名:汤清明申请学位级别:硕士专业:概率论与数理统计指导教师:岳荣先201203中文摘要摘要本文讨论三变量随机系数回归模型,二阶两变量随机系数模型的最优设计,,证明了该类模型的最优设计可在设计域的八个顶点处获得,采用matlab编程给出A一,D一,仇一最优设计的数值结果,,研究二阶两变量随机系数回归模型正交设计,旋转设计,,但其旋转设计一般是不存在的,若该模型是随机截距模型,则设计具有旋转性,,在D一,A一准则下,星号臂长1取无穷大时,该设计同时为D一,,以真实模型是二阶单变量随机系数回归模型,拟合模型是一阶单变量随机系数回归模型为例,在预测均方误差最小的准则下,给出试验的设计方案,,:随机系数回归模型,最优设计,洛纳序,中心组合设计,稳健设计第1页AbstractThispaperisconcernedwiththeoptimaldesignforthethreevariablesrandomcoefficientregressionmodelsandsecond·orderbivariaterandomcoefficientregressionmodels,—tremesettingsoftheunitcube,,someoptimaldesignsunderthecriteriaoforthog-onality,rotatability,D—andA—forsecond-’Sclearthattherandomeffectdoes110businesswiththeorthogonaldesign,andtherotatabledesignoftennotexistexceptfortheinterceptcoefficientisrandom;Also,underthecriteriaofD—andA一,-orderrandomcoefficientregressionmodel,-squarederrorcriterion,pletelyandtheexperimentdesignSOastOminimizebiasalone,KeyWords:Randomcoefficientregressionmodel,Optimaldesign,positedesign,????????????????????.????????????????????.????????????????????=2的中心组合设计方案?????????????????????