追加数据对条件指数的影响

详细信息

On Effects of Augmentation of data on Condition Index

Funds:

Project supported partially by National Natural Science Foundation of China.

摘要: 克服线性回归模型中设计矩阵的复共线性,主要有三种方法:追加数据,自变量选择和非最小二乘法,本文研究追加数据在减少条件数中的作用,我们的研究表明,在可能情况下适当地选择追加数据,设计矩阵的条件指数可以被减少.我们用在回归最优设计中广泛被研究过的Gaylor-Merrill数据说明了本文理论结果的实用意义。
- 条件数 /
- 条件指标 /
- 多重共线性
Abstract: There are three approaches in the literature to remedy the multicollinearity in design matrix in a linear regression: augmentation of data, variable selection and alternative procedures to the ordinary least squares. In this note our emphasis is focused on the effect of augmentation of data on condition index. Our results show that when the additional data are properly chosen in practical possible situation, the condition index of design matrix can be reduced. the results obtained here are illustrated by Gaylor-Merrill data [1] which has been extensively discussed in the literature on regression optimal design.
- Condition number /
- Condition index /
- Multicollinearity