Garthwaite, Paul H.; Critchley, Frank; Anaya Izquierdo, Karim and Mubwandarikwa, Emmanuel
(2012).
| DOI (Digital Object Identifier) Link: | https://doi.org/10.1093/biomet/ass041 |
|---|---|
| Google Scholar: | Look up in Google Scholar |
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 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: | 02 May 2018 13:44 |
| URI: | http://oro.open.ac.uk/id/eprint/34730 |
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