一阶回归模型下Q和Q_B准则的几个结果

SOME RESULTS ON Q AND Q_B CRITERIA UNDER THE FIRST ORDER REGRESSION MODEL

在试验设计中,一阶回归模型通常被作为合格拟合模型用来从众多因子中筛选出效应显著的特殊因子,而Q和Q_B准则能够比较简单地从大量的合格拟合模型中找出具有最优性质的设计.主要探讨了当拟合模型为一阶回归模型时,二水平的初始设计d与其Double设计(d d d -d)在Q和Q_B准则下的最优关系.给出了初始设计d的Q和Q_B值与其Double设计的Q和Q_B值之间的解析关系,从而得到在Q或Q_B准则下如果初始设计d是最优的,那么其Double设计也是最优的.此外,也分别给出了初始设计d及其Double设计的Q值和Q_B值的一个下界.

In experimental design,the first order regression model has been usually used to screen a few important main effects from a large number of potential factors.The so-called Q and Q_b criteria can find optimal designs from many eligible model uncertainty.This paper aims to explore the optimal relationship of Q and Qb criteria between the original design d with two levels and its double design D_d under the first order regression model,where D_d =（d d d -d）. A new analytical relation between Q-values or Q_B-values of d and D_d is obtained,which shows that under Q criterion or Q_b criterion,if d is optimal,then D_d is also optimal.Moreever,some lower bounds on Q-values and Q_B-values of d and D_d are also derived,respectively.