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The General Linear Test in the Ridge Regression

  • Bae, Whasoo (Department of Data Science/Institute of Statistical Information, Inje University) ;
  • Kim, Minji (Department of Statistics, Pusan National University) ;
  • Kim, Choongrak (Department of Statistics, Pusan National University)
  • Received : 2014.03.19
  • Accepted : 2014.05.22
  • Published : 2014.07.31

Abstract

We derive a test statistic for the general linear test in the ridge regression model. The exact distribution for the test statistic is too difficult to derive; therefore, we suggest an approximate reference distribution. We use numerical studies to verify that the suggested distribution for the test statistic is appropriate. A asymptotic result for the test statistic also is considered.

Keywords

References

  1. Chipman, J. S. and Rao, M. M. (1964). The treatment of linear restriction in regression analysis, Econometrica, 32, 198-209. https://doi.org/10.2307/1913745
  2. Harville, D. A. (2008). Matrix Algebra from a Statistician's Perspective, Springer.
  3. Hoerl, A. E. and Kennard, R. W. (1970). Ridge regression: Biased estimation for non-orthogonal problems, Technometrics, 12, 55-67. https://doi.org/10.1080/00401706.1970.10488634
  4. Hoerl, A. E. and Kennard, R. W. (1990). Ridge regression: Degrees of freedom in the analysis of variance, Communications in Statistics-Simulation and Computation, 19, 1485-1495. https://doi.org/10.1080/03610919008812931
  5. Kim, C. and Kang, K. (2010). Regression Analysis, Kyowoosa, Seoul.
  6. Neter, J., Wasserman, W. and Kutner, M. H. (1990). Applied Linear Statistical Models, Irwin, Boston.
  7. Obenchain, R. L. (1977). Classical F-tests and confidence regions for ridge regression, Technometrics, 19, 429-439. https://doi.org/10.1080/00401706.1977.10489582
  8. Seber, G. A. F. and Lee, A. J. (2003). Linear Regression Analysis, Wiley, New York.
  9. Wahba, G., Golub, G. H. and Heath, M. T. (1979). Generalized cross-validation as a method for choosing a good ridge parameter, Technometrics, 21, 215-223. https://doi.org/10.1080/00401706.1979.10489751