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.
Keywords
RidgeMathematicsResidualDiagonalRegressionStatisticsLeast-squares function approximationApplied mathematicsAlgorithmGeometryGeology
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Publication Info
- Year
- 1970
- Type
- article
- Volume
- 12
- Issue
- 1
- Pages
- 55-67
- Citations
- 8164
- Access
- Closed
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Cite This
Arthur E. Hoerl,
Robert W. Kennard
(1970).
Ridge Regression: Biased Estimation for Nonorthogonal Problems.
Technometrics
, 12
(1)
, 55-67.
https://doi.org/10.1080/00401706.1970.10488634
Identifiers
- DOI
- 10.1080/00401706.1970.10488634