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### 一类二阶模型下中心复合设计的预测方差

1. 1. 江苏理工学院数理学院, 常州 213001;
2. 中央财经大学统计与数学学院, 北京 102206
• 收稿日期:2022-03-17 修回日期:2022-06-02 发布日期:2022-12-13
• 通讯作者: 陈雪平, Email: chenxueping@jsut.edu.cn
• 基金资助:
国家自然科学基金项目(11971204), 江苏省自然科学基金(BK20200108), 江苏理工学院中吴青年创新人才支持计划.

Yan Jing, Chen Xueping, Zhang Minjue, Wang Xiaodi. Prediction Variance Analysis of a Class of Central Composite Designs Under the Second-Order Model[J]. Journal of Systems Science and Mathematical Sciences, 2022, 42(11): 3107-3118.

### Prediction Variance Analysis of a Class of Central Composite Designs Under the Second-Order Model

Yan Jing1, Chen Xueping1, Zhang Minjue1, Wang Xiaodi2

1. 1. School of Mathematics and Physics, Jiangsu University of Technology, Changzhou 213001;
2. School of Statistics and Mathematics, Central University of Finance and Economics, Beijing 102206
• Received:2022-03-17 Revised:2022-06-02 Published:2022-12-13

Prediction ability is an important criterion to evaluate the quality of design and model selection. The prediction accuracy in a certain area can be accurately obtained through the prediction variance function. This paper first introduces the recently proposed central composite design based on orthogonal-array and the modified designs based on Minimax criterion, and then gives the analytical expressions of the average predictive variance function, minimum predictive variance function and maximum predictive variance function of these two kinds of designs for a given sphere. The results show that they are only the functions of sphere distance and the design parameters. It can provide an important reference for practical workers in prediction.

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