The DOI matches its Crossref record; 6 of the 6 references it cites were found in a registry or an index.
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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Cites
A new look at the statistical model identification
Akaike, H. (1974) · IEEE Transactions on Automatic Control · doi:10.1109/tac.1974.1100705 · Cited by 51,879
Craven, P., & Wahba, G. (1978) · Numerische Mathematik · doi:10.1007/bf01404567 · Cited by 3,388
Self-citationSingular value decomposition and least squares solutions
Golub, G. H., & Reinsch, C. (1970) · Numerische Mathematik · doi:10.1007/bf02163027 · Cited by 2,929 · cited 2×
“The E1 were generated as pseudo-random m.(O, u 2) independent r.v.'s, V(X) was computed using the right-hand side of(2.3) and the Golub-Reinsch singu lar value decomposition [16].”
InfluentialSelf-citationThe Predictive Sample Reuse Method with Applications
Geisser, S. (1975) · Journal of the American Statistical Association · doi:10.1080/01621459.1975.10479865 · Cited by 2,748 · cited 2×
“This estimate is a rotation-invariant version of Allen's PRESS or ordinary cross-validation, as described in Hocking's discussion to Stone's paper [36] (see also Allen [3], and Geisser [13]).”
Bayes Estimates for the Linear Model
Lindley, D. V., & Smith, A. F. M. (1972) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1972.tb00885.x · Cited by 2,025
The Relationship Between Variable Selection and Data Agumentation and a Method for Prediction
Allen, D. M. (1974) · Technometrics · doi:10.1080/00401706.1974.10489157 · Cited by 1,469 · cited 1×
“This estimate is a rotation-invariant ver sion of Allen's PRESS or ordinary cross-validation, as described in Hocking's discussion to Stone's paper [36] (see also Allen [3], and Geisser [13]).”
Cited by
Deep learning in neural networks: an overview
Schmidhuber, J. (2015) · Neural Networks · doi:10.1016/j.neunet.2014.09.003 · Cited by 18,570
Analysis of Discrete Ill-Posed Problems by Means of the L-Curve
Hansen, P. C. (1992) · SIAM Review · doi:10.1137/1034115 · Cited by 3,903
Craven, P., & Wahba, G. (1978) · Numerische Mathematik · doi:10.1007/bf01404567 · Cited by 3,388
Self-citationWold, S., Ruhe, A., Wold, H., & Dunn, III (1984) · SIAM Journal on Scientific and Statistical Computing · doi:10.1137/0905052 · Cited by 2,529
Interpreting magnetic fields of the brain: minimum norm estimates
Hämäläinen, M. S., & Ilmoniemi, R. J. (1994) · Medical & Biological Engineering & Computing · doi:10.1007/bf02512476 · Cited by 1,995
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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