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

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.