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The extension of generalized cross-validation to a multi-parameter class of estimators

Published online by Cambridge University Press:  17 February 2009

D. M. O'Brien  and
J. N. Holt
D. M. O'Brien
Affiliation:
Department of Mathematical Physics, University of Adelaide, Adelaide, South Australia 5000
J. N. Holt
Affiliation:
Department of Mathematics, University of Queensland, St. Lucia, Queensland 4067
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Abstract

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The method of generalized cross-validation (GCV) provides a good value for the “ridge” regularization parameter for an ill-conditioned linear system, such as the system produced by discretization of a Fredholm integral equation of the first kind. In this note we apply GCV to a wider class of estimators than the one parameter ridge estimators. We observe that the expected values of the parameter mean-square error, the predictive mean-square error, and the GCV function are simultaneously minimized over this new class, so we accept the minimizer of the GCV function as the best computable estimator. We present a simple algorithm for computing this estimator from the data, so that a numerical search is not needed.

Type
Research Article
Information
The ANZIAM Journal , Volume 22 , Issue 4 , April 1981 , pp. 501 - 514
Copyright
Copyright © Australian Mathematical Society 1981

References

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