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The efficient cross-validation of principal components applied to principal component regression |
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| Authors: | Bart Mertens Tom Fearn Michael Thompson |
| Institution: | (1) Department of Chemistry, Birkbeck College, Gordon House, 29 Gordon Square, WC1H 0PP London, UK;(2) Department of Statistical Science, University College London, Gower Street, WC1E 6BT London, UK |
| Abstract: | The cross-validation of principal components is a problem that occurs in many applications of statistics. The naive approach of omitting each observation in turn and repeating the principal component calculations is computationally costly. In this paper we present an efficient approach to leave-one-out cross-validation of principal components. This approach exploits the regular nature of leave-one-out principal component eigenvalue downdating. We derive influence statistics and consider the application to principal component regression. |
| Keywords: | Cross-validation downdating eigenproblem eigenvalue influence statistics principal components regression |
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