Abstract
For testing general linear hypotheses in multiple regression models. it is shown that non-stochastically shrunken ridge estimators yield the same central F-ratios and t-statistics as does the least squares estimator. Thus although ridge regression does produce biased point estimates which deviate from the least squares solution, ridge techniques do not generally yield "new" normal theory statistical inferences: in particular, ridging does not necessarily produce "shifted" confidence regions. A concept, the ASSOCIATFD PROBABILITY of a ridge estimate, is defined using the usual, hyperellipsoidal confidence region centered at the least squares estimator, and it is argued that ridge estimates are of relatively little interest when they are so "extreme" that they lie outside of the least squares region of say 90 percent confidence.
Keywords
RidgeStatisticsEstimatorMathematicsConfidence intervalLeast-squares function approximationGeneralized least squaresRegressionConfidence regionRegression analysisTotal least squaresLinear regressionEconometricsGeographyCartography
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Publication Info
- Year
- 1977
- Type
- article
- Volume
- 19
- Issue
- 4
- Pages
- 429-439
- Citations
- 75
- Access
- Closed
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Cite This
Robert L. Obenchain
(1977).
Classical F-Tests and Confidence Regions for Ridge Regression.
Technometrics
, 19
(4)
, 429-439.
https://doi.org/10.1080/00401706.1977.10489582
Identifiers
- DOI
- 10.1080/00401706.1977.10489582