KMS Of Academy of mathematics and systems sciences, CAS
The comparison between polynomial regression and orthogonal polynomial regression | |
Tian, GL | |
1998-07-01 | |
Source Publication | STATISTICS & PROBABILITY LETTERS |
ISSN | 0167-7152 |
Volume | 38Issue:4Pages:289-294 |
Abstract | 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. |
Keyword | condition number gram-Schmidt decomposition multicollinearity optimal design polynomial regression |
Language | 英语 |
WOS Research Area | Mathematics |
WOS Subject | Statistics & Probability |
WOS ID | WOS:000074314000001 |
Publisher | ELSEVIER SCIENCE BV |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/13332 |
Collection | 中国科学院数学与系统科学研究院 |
Affiliation | Acad Sinica, Inst Appl Math, Beijing 100080, Peoples R China |
Recommended Citation 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. |
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