二次随机系数回归模型的A-最优设计  

A-optimal design of quadratic random coefficient regression model

作　　者：程靖[1] 岳荣先[2] 

机构地区：[1]安徽农业大学理学院,安徽合肥230036 [2]上海师范大学数理学院,上海200234

出　　处：《上海师范大学学报（自然科学版）》2017年第2期195-199,共5页Journal of Shanghai Normal University(Natural Sciences)

基　　金：国家自然科学基金(11401056;11471216);安徽省环保厅项目(2015-5);安徽农业大学稳定与引进人才项目(yj2015-27)

摘　　要：研究了单位设计域上二次随机系数回归模型在恒等设计类中的A-最优设计.首先证明了A-最优设计准则满足洛纳偏序性质;利用A-最优设计准则的洛纳偏序性质,证明了单位设计域上的二次随机系数回归模型在恒等设计类中的A-最优设计可以在包含设计域两个端点0,1在内的3个设计点上获得;进而给出了二次随机系数回归模型A-最优恒等设计的精确结果.结果表明,二次随机系数回归模型在恒等设计类中的A-最优设计不受到随机效应项的方差影响,其A-最优设计的第三个谱点位置接近单位设计域的中点,且在该点处的A-最优设计权重接近于0.5.A-optimal identical design of quadratic random coefficient regression model on the design domain of [0,1 ] is constructed in this paper. Loewner order character of A-optimal criterion is proved in the paper and it is proved that A-optimal identical design of quadratic random coefficient regression model could be obtained on three design points including the two extreme set-tings of the design domain of [0,1 ]. Accurate result of A-optimal identical design of quadratic random coefficient regression mod-el is given in the paper. The result shows that A-optimal identical design of quadratic random coefficient regression model does not depend on the variances of the random effects. The result also shows that the third spectral point of A-optimal design is near the midpoint of the design domain of [0,1 ] and i t ’s weight coefficient of A-optimal design is near 0. 5.

关 键 词：A-最优设计 二次回归 随机系数 恒等设计 

分 类 号：O212.6[理学—概率论与数理统计]