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2011 | OriginalPaper | Chapter

Ridge and Surrogate Ridge Regressions

Author : Ali S. Hadi

Published in: International Encyclopedia of Statistical Science

Publisher: Springer Berlin Heidelberg

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Excerpt

Ridge regression is a method for the estimation of the parameters of a linear regression model (see Linear Regression Models) which is useful when the predictor variables are highly collinear, that is, when there is a strong linear relationship among the predictor variables. Hoerl (1959) named the method ridge regression because of its similarity to ridge analysis used in his earlier work to study second-order response surfaces in many variables. Some standard references for ridge regression are Hoerl and Kennard (1970, 1976), Belsley et al. (1980), and Chatterjee and Hadi (2006). …

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previous chapter Response Surface Methodology
next chapter Rise of Statistics in the Twenty First Century
Literature
Belsley DA, Kuh E, Welsch RE (1980) Regression diagnostics: identifying influential data and sources of collinearity. Wiley, New YorkMATH
Chatterjee S, Hadi AS (2006) Regression analysis by example, 4th edn. Wiley, New YorkMATH
Dorugade AV, Kashid DN (2010) Alternative method for choosing ridge parameter for regression. Appl Math Sci 4:447–456MATHMathSciNet
Golub GH, van Loan C (1989) Matrix computations. John Hopkins, BaltimoreMATH
Hoerl AE (1959) Optimum solution of many variables. Chem Eng Prog 55:69–78
Hoerl AE (1962) Application of ridge analysis to regression problems. Chem Eng Prog 58:54–59
Hoerl AE, Kennard RW (1970) Ridge regression: biased estimation for nonorthogonal problems. Technometrics 12:55–68MATH
Hoerl AE, Kennard RW (1976) Ridge regression: iterative estimation of the biasing parameter. Commun Stat, Theory Methods A5:77–88
Hoerl AE, Kennard RW (1981) Ridge regression – 1980: advances, algorithms, and applications. Am J Math Manag Sci 1:5–83MathSciNet
Hoerl AE, Kennard RW, Baldwin KF (1975) Ridge regression: some simulations. Commun Stat, Theory Methods 4:105–123MATH
Jensen DR, Ramirez DE (2008) Anomalies in the foundations of ridge regression. Int Stat Rev 76:89–105MATH
Khalaf G, Shukur G (2005) Choosing ridge parameter for regression problem. Commun Stat, Theory Methods 34:1177–1182MATHMathSciNet
Lawless JF, Wang P (1976) A simulation study of ridge and other regression estimators. Commun Stat, Theory Methods 14:1589–1604
Masuo N (1988) On the almost unbiased ridge regression estimation. Commun Stat, Simul 17:729–743MATH
Wahba G, Golub GH, Health CG (1979) Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics 21:215–223MATHMathSciNet
Metadata
Title
Ridge and Surrogate Ridge Regressions
Author
Ali S. Hadi
Copyright Year
2011
Publisher
Springer Berlin Heidelberg
Book
International Encyclopedia of Statistical Science

Print ISBN: 978-3-642-04897-5

Electronic ISBN: 978-3-642-04898-2

Copyright Year: 2011

DOI
https://doi.org/10.1007/978-3-642-04898-2_493