| 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. |
| 关键词: A-最优设计 二次回归 随机系数 恒等设计 |
| DOI：10.3969/J.ISSN.100-5137.2017.02.004 |
| 分类号: |
| 基金项目: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） |
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| A-optimal design of quadratic random coefficient regression model |
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Cheng Jing1, Yue Rongxian2
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1.College of Science, Anhui Agricultural University, Hefei, Anhui 230036, China;2.College of Mathematics and Science, Shanghai Normal University, Shanghai 200234, China
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| Abstract: |
| 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 settings of the design domain of [0,1].Accurate result of A-optimal identical design of quadratic random coefficient regression model 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 it's weight coefficient of A-optimal design is near 0.5. |
| Key words: A-optimal design quadratic regression random coefficient identical design |
