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Ridge regression
Abstract
Ridge regression is a popular parameter estimation method used to address the collinearity problem frequently arising in multiple linear regression. The formulation of the ridge methodology is reviewed and properties of the ridge estimates capsulated. In particular, four rationales leading to a regression estimator of the ridge form are summarized. Algebraic properties of the ridge regression coefficients are given, which elucidate the behavior of a ridge trace for small values of the ridge parameter (i.e., close to the least squares solution) and for large values of the ridge parameter. Further properties involving coefficient sign changes and rates‐of‐change, as functions of the ridge parameter, are given for specific correlation structures among the independent variables. These results help relate the visual behavior of a ridge trace to the underlying structure of the data. Copyright © 2009 John Wiley & Sons, Inc. This article is categorized under:Statistical Models > Linear Models Algorithms and Computational Methods > Least Squares
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Cites
Regression shrinkage and selection via the lasso
Tibshirani, R. (1996) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1996.tb02080.x · Cited by 51,482
The Elements of Statistical Learning
Hastie, T., Friedman, J., & Tibshirani, R. (2001) · Springer Series in Statistics · doi:10.1007/978-0-387-21606-5 · Cited by 24,162
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Alin, A. (2010) · WIREs Computational Statistics · doi:10.1002/wics.84 · Cited by 928
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Yang, B., Guneri, D., Yu, H., Wright, E. P., Chen, W., Waller, Z. A. E., & Ding, Y. (2024) · Nucleic Acids Research · doi:10.1093/nar/gkae092 · Cited by 29
Xia, Y., Du, X., Liu, B., Guo, S., & Huo, Y.-X. (2024) · Nucleic Acids Research · doi:10.1093/nar/gkae429 · Cited by 31
Detection of Cyber Grooming in Online Conversation
Bours, P., & Kulsrud, H. (2019) · 2019 IEEE International Workshop on Information Forensics and Security (WIFS) · doi:10.1109/wifs47025.2019.9035090 · Cited by 27
Utilizing Social Clustering-Based Regression Model for Predicting Student’s GPA
Hassan, Y. M. I., Elkorany, A., & Wassif, K. (2022) · IEEE Access · doi:10.1109/access.2022.3172438 · Cited by 15
Metadata
- Authors
- McDonald, G. C.
- Venue
- WIREs Computational Statistics
- Publisher
- Wiley
- Published
- 2009-07
- Volume
- 1
- Issue
- 1
- Pages
- 93-100
- ISSN
- 1939-0068 (ISSN-L)
- 1939-5108
- OpenAlex
- W4244230525
- Cited by
- 823
- References
- 2
- FWCI
- 1.09
- Type
- journal article
- Language
- en
- Open access
- closed
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