Skip to main content

Confidence Intervals for Ridge Regression Parameters

  • Chapter

Part of the book series: The University of Western Ontario Series in Philosophy of Science ((WONS,volume 36))

Abstract

This paper reviews various alternatives for constructing confidence intervals for ridge regression (RR) parameters, and illustrates them with an example. Among the newer alternatives are bootstrapping and those based on Stein’s (1981) unbiased estimate of the mean squared error (MSE) of a biased estimator of multivariate normal mean. A simulation study supports the validity of the confidence statements based on Stein’s model as modified here for the ridge regression problem. It yields confidence intervals which can be more useful and reliable than those based on other methods.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Baranchik, A. J. (1970), “A family of minimax estimators of the mean of a multi-variate normal distribution”. Annals of Mathematical Statistics 41, 642–645.

    Article  MathSciNet  Google Scholar 

  • Berger, J. (1980), “A robust generalized Bayes estimator and confidence region for a multivariate normal mean”. Annals of Statistics 8, 716–761.

    Article  MathSciNet  MATH  Google Scholar 

  • Efron, B. (1982), The Jackknife, the Bootstrap and Other Resampling Plans. Philadelphia: Society for Industrial and Applied Mathematics (SIAM), Vol. 38.

    Google Scholar 

  • Efron, B., and C. Morris (1972), “Limiting the risk of Bayes and empirical Bayes estimators—Part II: The empirical Bayes case”. Journal of the American Statistical Association 67, 130–139.

    Article  MathSciNet  MATH  Google Scholar 

  • Hald, A. (1952), Statistical Theory with Engineering Applications. New York: Wiley and Sons.

    MATH  Google Scholar 

  • Hoerl, A. E., and R. W. Kennard (1970), “Ridge regression: biased estimation for nonorthogonal problems”. Technometrics 12, 55–67.

    Article  MATH  Google Scholar 

  • Hoerl, A. E., R. W. Kennard, and K. F. Baldwin (1975), “Ridge regression: some simulations”. Communications in Statistics 4, 105–123.

    Article  Google Scholar 

  • Johnson, N. L., and S. Kotz (1970), Continuous Univariate Distributions 1 and 2. New York: Wiley and Sons.

    Google Scholar 

  • Kabe, D. G. (1983), “A quadratic programming approach to the construction of simultaneous confidence intervals”. Communications in Statistics A, Theory and Methods 12, 2053–2058.

    Article  MathSciNet  MATH  Google Scholar 

  • Mallows, C. L. (1973), “Some comments on C p.” Technometrics 15, 661–675.

    Article  MATH  Google Scholar 

  • Morris, C. N. (1983), “Parametric empirical Bayes inference: theory and applications”. Journal of the American Statistical Association 78, 47–55.

    Article  MathSciNet  MATH  Google Scholar 

  • Obenchain, R. L. (1975), “Ridge analysis following a preliminary test of the shrunken hypothesis”. Technometrics 17, 431–441.

    Article  MathSciNet  MATH  Google Scholar 

  • Obenchain, R. L. (1977), “Classical F-tests and confidence regions for ridge regression”. Technometrics 19, 429–439.

    Article  MathSciNet  MATH  Google Scholar 

  • Peters, S. C., and D. A. Preedman (1984), “Some notes on the bootstrap in regression problems”. Journal of Business and Economic Statistics 2, 406–409.

    Article  Google Scholar 

  • Rao, C. R. (1973), Linear Statistical Inference and Its Applications, 2nd edition. New York: Wiley and Sons.

    Book  MATH  Google Scholar 

  • Schenker, N. (1985), “Qualms about bootstrap confidence intervals”. Journal of the American Statistical Association 80, 360–361.

    Article  MathSciNet  Google Scholar 

  • Stein, C. (1981), “Estimation of the mean of a multivariate normal distribution”. Annals of Statistics 9, 1135–1151.

    Article  MathSciNet  MATH  Google Scholar 

  • Vinod, H. D. (1976), “Application of new ridge regression methods to a study of Bell System scale economies”. Journal of the American Statistical Association 71, 835–841.

    Article  Google Scholar 

  • Vinod, H. D. (1978), “A survey of ridge regression and related techniques for improvements over ordinary least squares”. Review of Economics and Statistics 60, 121–131.

    Article  MathSciNet  Google Scholar 

  • Vinod, H. D. (1980), “New confidence intervals for ridge regression parameters”. Bell Laboratories Economics Discussion Paper No. 172, Murray Hill, N. J.

    Google Scholar 

  • Vinod, H. D., and B. Raj (1984), “Bootstrapping confidence intervals for arbitrary functions of regression parameters”. Working Paper 8413, Dept. of Economics, Fordham University, Bronx, New York 10458.

    Google Scholar 

  • Vinod, H. D., and A. Ullah (1981), Recent Advances in Regression Methods. New York: Marcel Dekker.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1987 D. Reidel Publishing Company

About this chapter

Cite this chapter

Vinod, H.D. (1987). Confidence Intervals for Ridge Regression Parameters. In: MacNeill, I.B., Umphrey, G.J., Carter, R.A.L., McLeod, A.I., Ullah, A. (eds) Time Series and Econometric Modelling. The University of Western Ontario Series in Philosophy of Science, vol 36. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4790-0_19

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-4790-0_19

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8624-0

  • Online ISBN: 978-94-009-4790-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics