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Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter
Abstract
Consider the ridge estimate (λ) for β in the model unknown, (λ) = (X T X + nλI)−1 X T y. We study the method of generalized cross-validation (GCV) for choosing a good value for λ from the data. The estimate is the minimizer of V(λ) given by where A(λ) = X(X T X + nλI)−1 X T . This estimate is a rotation-invariant version of Allen's PRESS, or ordinary cross-validation. This estimate behaves like a risk improvement estimator, but does not require an estimate of σ2, so can be used when n − p is small, or even if p ≥ 2 n in certain cases. The GCV method can also be used in subset selection and singular value truncation methods for regression, and even to choose from among mixtures of these methods.
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Metadata
- Authors
- Golub, G. H., Heath, M., & Wahba, G.
- Venue
- Technometrics
- Publisher
- Informa UK Limited
- Published
- 1979-05
- Volume
- 21
- Issue
- 2
- Pages
- 215-223
- ISSN
- 0040-1706 (ISSN-L)
- 1537-2723
- OpenAlex
- W1990381576
- Cited by
- 3,934
- References
- 6
- FWCI
- 19.28
- Type
- journal article
- Language
- en
- Open access
- closed
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