527
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

On the Strong Consistency of Ridge Estimates

, &
Pages 617-626 | Received 09 Jun 2012, Accepted 05 Nov 2012, Published online: 31 Dec 2014

References

  • Birkes, D., Dodge, Y. (1993). Alternative Methods of Regression. New York: John Wiley & Sons.
  • Brown, W.G., Beattie, B.R. (1975). Improving estimates of economic parameters by use of Ridge Regression with production function application. Amer. J. Agricult. Econ. 57:21–32.
  • Chow, Y.S., Teicher, H. (1997). Probability Theory: Independence, Interchangeability, Martingales. 3rd ed. New York: Springer.
  • Draper, N.R., Van Nostrand, R.C. (1979). Ridge regression and James-Stein estimation: review and comments. Technometrics 21:451–466.
  • Gui-Jing, C., Lai, T.L., Wei, C.Z. (1981). Convergence systems and strong, consistency of least squares estimates in regression models. J. Multivariate Anal. 11:319–333.
  • GuiJing, C. (1984). Extension of Lai-Robbins-Wei’s theorem. Acta Mathematicae Applicatae Sinica 1(1):2–7.
  • Harville, D.A. (1997). Matrix Algebra From a Statiscian’s Perspective. New York: Springer-Verlag.
  • Hoerl, A.E. (1962). Application of ridge analysis to regression problems. Chem. Eng. Progr. 58(3):54–59.
  • Horn, R.A., Johnson, C.R. (1985). Matrix Analysis. Cambridge: Cambridge University Press.
  • Lai, T.L., Robbins, H., Wei, C.Z. (1979). Strong consistency of least squares estimates in multiple regression II. J. Multivariate Anal. 9:343–362.
  • Lita da Silva, J., Mexia, J.T. (2013). Strong consistency of least squares estimates with i.i.d. errors with mean values not necessarily defined. Statistics 47(4):707–714.
  • Makarov, B.M., Goluzina, M.G., Lodkin, A.A., Podkorytov, A.N. (1992). Selected Problems in Real Analysis. ProvidenceRI: American Mathematical Society.
  • Murteira, B., Ribeiro, C.S., Andrade e Silva, J., e Pimenta, C. (2002). Introdução à Estatística. Lisbon, Portugal: McGraw-Hill.
  • Van Nostrand, R.C. (1980). Comment on “A critique of some ridge regression methods” by G. Smith and F. Campbell. J. Amer. Statist. Assoc. 75:92–94.
  • Vinod, H.D. (1976). Simulation and extension of a minimum mean squared error estimator in comparison with Stein’s. Technometrics 18:491–496.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.