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Ridge Regression: Biased Estimation for Nonorthogonal Problems
Abstract
In multiple regression it is shown that parameter estimates based on minimum residual sum of squares have a high probability of being unsatisfactory, if not incorrect, if the prediction vectors are not orthogonal. Proposed is an estimation procedure based on adding small positive quantities to the diagonal of X′X. Introduced is the ridge trace, a method for showing in two dimensions the effects of nonorthogonality. It is then shown how to augment X′X to obtain biased estimates with smaller mean square error.
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Cited by
Computationally efficient whole-genome regression for quantitative and binary traits
Mbatchou, J., Barnard, L., Backman, J., Marcketta, A., Kosmicki, J. A., Ziyatdinov, A., Benner, C., O’Dushlaine, C., Barber, M., Boutkov, B., et al. (2021) · Nature Genetics · doi:10.1038/s41588-021-00870-7 · Cited by 1,502
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
Tanaka, J. S. (1987) · Child Development · doi:10.2307/1130296 · Cited by 982
Ridge regression:some simulations
Hoerl, A. E., Kannard, R. W., & Baldwin, K. F. (1975) · Communications in Statistics · doi:10.1080/03610927508827232 · Cited by 873
Self-citationNielsen, A. A. (2007) · IEEE Transactions on Image Processing · doi:10.1109/tip.2006.888195 · Cited by 746
Metadata
- Authors
- Hoerl, A. E., & Kennard, R. W.
- Venue
- Technometrics
- Publisher
- Taylor & Francis
- Published
- 1970-02-01
- Volume
- 12
- Issue
- 1
- Pages
- 55-55
- ISSN
- 0040-1706 (ISSN-L)
- OpenAlex
- W4255455317
- Cited by
- 1,955
- References
- 0
- FWCI
- 3.47
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: Ridge Regression: Biased Estimation for Nonorthogonal Problems. https://app.cochat.ai/papers/10.2307/1267351
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- Hoerl, A. E., & Kennard, R. W. (1970). Ridge Regression: Biased Estimation for Nonorthogonal Problems. Technometrics. https://doi.org/10.2307/1267351
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