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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: http://dx.doi.org/10.1093/biomet/ass041
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Abstract

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 Article
Copyright Holders: 2012 Biometrika Trust
ISSN: 1464-3510
Keywords: cos-max; cos-square; cilution; matrix decomposition; multivariate Chebychev inequality; variance inflation factor.
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 34730
Depositing User: Frank Critchley
Date Deposited: 24 Oct 2012 15:30
Last Modified: 25 Oct 2013 09:41
URI: http://oro.open.ac.uk/id/eprint/34730
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