The comparison between polynomial regression and orthogonal polynomial regression

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	The comparison between polynomial regression and orthogonal polynomial regression
	Tian, GL
	1998-07-01
发表期刊	STATISTICS & PROBABILITY LETTERS
ISSN	0167-7152
卷号	38 期号:4 页码:289-294
摘要	In this paper, the relationship between X, the structure matrix in a polynomial regression (PR) model, and Z, the structure matrix in an orthogonal polynomial regression (OPR) model, is established. We show that C(X) greater than or equal to C(Z), where C(X) denotes the condition number of X, and OPR is superior to PR under the criteria of A- and E- optimalities in the sense of experimental design. However, the two regressions are equivalent under the criterion of D-optimality. These conclusions are also valid for the general linear regression model with p(> 1) predictor variables. (C) 1998 Elsevier Science B.V. All rights reserved.
关键词	condition number gram-Schmidt decomposition multicollinearity optimal design polynomial regression
语种	英语
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000074314000001
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/13332
专题	中国科学院数学与系统科学研究院
作者单位	Acad Sinica, Inst Appl Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Tian, GL. The comparison between polynomial regression and orthogonal polynomial regression[J]. STATISTICS & PROBABILITY LETTERS,1998,38(4):289-294.
APA	Tian, GL.(1998).The comparison between polynomial regression and orthogonal polynomial regression.STATISTICS & PROBABILITY LETTERS,38(4),289-294.
MLA	Tian, GL."The comparison between polynomial regression and orthogonal polynomial regression".STATISTICS & PROBABILITY LETTERS 38.4(1998):289-294.