一类二阶模型下中心复合设计的预测方差  

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

作　　者：严静 陈雪平 张敏珏 王晓迪 YAN Jing;CHEN Xueping;ZHANG Minjue;WANG Xiaodi(School of Mathematics and Physics,Jiangsu University of Technology,Changzhou 213001;School of Statistics and Mathematics,Central University of Finance and Economics,Beijing 102206)

机构地区：[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

出　　处：《系统科学与数学》2022年第11期3107-3118,共12页Journal of Systems Science and Mathematical Sciences

基　　金：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。

摘　　要：预测能力是评价设计优劣、模型选择的一个重要准则,通过预测方差函数可以准确获得在一定区域内的预测精度.文章首先介绍了最新提出的基于正交表的中心复合设计以及基于极小极大准则的改进设计,然后详细给出了两类设计在给定球面上的平均预测方差函数、最小预测方差函数和最大预测方差函数的解析表达式,其仅为球距和设计参数的函数,这一结果可以为实际工作者在预测分析时提供重要参考.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.

关 键 词：试验设计 预测方差 响应曲面设计 正交表 极小极大准则 

分 类 号：O212.6[理学—概率论与数理统计]