The Open UniversitySkip to content

Orthogonalization of vectors with minimal adjustment

Garthwaite, Paul H.; Critchley, Frank; Anaya Izquierdo, Karim and Mubwandarikwa, Emmanuel (2012). Orthogonalization of vectors with minimal adjustment. Biometrika, 99(4) pp. 787–798.

DOI (Digital Object Identifier) Link:
Google Scholar: Look up in Google Scholar


Two transformations are proposed that give orthogonal components with a one-to-one correspondence between the original vectors and the components. The aim is that each component should be close to the vector with which it is paired, orthogonality imposing a constraint. The transformations lead to a variety of new statistical methods, including a unified approach to the identification and diagnosis of collinearities, a method of setting prior weights for Bayesian model averaging, and a means of calculating an upper bound for a multivariate Chebychev inequality. One transformation has the property that duplicating a vector has no effect on the orthogonal components that correspond to nonduplicated vectors, and is determined using a new algorithm that also provides the decomposition of a positive-definite matrix in terms of a diagonal matrix and a correlation matrix. The algorithm is shown to converge to a global optimum.

Item Type: Journal Item
Copyright Holders: 2012 Biometrika Trust
ISSN: 1464-3510
Keywords: cos-max; cos-square; cilution; matrix decomposition; multivariate Chebychev inequality; variance inflation factor.
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 34730
Depositing User: Frank Critchley
Date Deposited: 24 Oct 2012 15:30
Last Modified: 07 Dec 2018 10:08
Share this page:


Altmetrics from Altmetric

Citations from Dimensions

Actions (login may be required)

Policies | Disclaimer

© The Open University   contact the OU