Cited by 9,648Advanced Statistical Methods and ModelsStatistical and numerical algorithmsStatistical Methods and Applications

Ridge regression: Biased estimation for nonorthogonal problems

Hoerl, Arthur E., Kennard, Robert W.·1970·Technometrics

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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Crossref · 10.1080/00401706.1970.10488634

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11 of 11 references verified0 citation errors · 0 not checkable

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  • A linear support vector machine is used for classifying gender, and ridge regression for predicting age and each personality factor.

    “We use a linear support vector machine (SVM) [92] for classifying the binary variable of gender, and ridge regression [93] for predicting age and each factor of personality.”

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Authors
Hoerl, A. E., & Kennard, R. W.
Affiliations
DuPont (United States) (US)
Venue
Technometrics
Published
1970-02
Volume
12
Issue
1
Pages
55-67
ISSN
  • 0040-1706 (ISSN-L)
  • 1537-2723
OpenAlex
W4234698323
Cited by
9,648
References
11
Citations by year
2026: 1338 · 2025: 968 · 2024: 720 · 2023: 738 · 2022: 728 · 2021: 772 · 2020: 647 · 2019: 553 · 2018: 484 · 2017: 293 · 2016: 283 · 2015: 269 · 2014: 250 · 2013: 238 · 2012: 218
FWCI
8.87
Type
journal article
Language
en
Open access
closed
Locations
Technometrics (publishedVersion)
Topics
  • Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
  • Physical Sciences › Mathematics › Applied Mathematics › Statistical and numerical algorithms
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
Keywords
ridge regression, biased estimation, multicollinearity, mean squared error, parameter estimation, multiple linear regression

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