Abstract
Generalized cross-validation is a method for choosing the smoothing parameter in smoothing splines and related regularization problems. This method requires the global minimization of the generalized cross-validation function. In this paper an algorithm based on interval analysis is presented to find the globally optimal value for the smoothing parameter, and a numerical example illustrates the performance of the algorithm.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Bates D.M., Lindstrom M.J., Wahba G., and Yandell B.S. 1987. GCVPAK-routines for generalized cross validation. Communications in Statistics-Simulation and Computation 16: 263–297.
Craven P. and Wahba G. 1979. Smoothing noisy data with spline functions. Numerische Mathematik 31: 377–390.
Cressie N.A.C. 1993. Statistics for Spatial Data, 2nd edn. New York, Wiley.
Girard D.A. 1998. Asymptotic comparision of (partial) crossvalidation, GCV and randomized GCV in nonparametric regression. Annals of Statistics 26: 315–334.
Golub G.H., Heath M., and Wahba G. 1979. Generalized cross validation as a method for choosing a good ridge parameter. Technometrics 21: 215–223.
Green P. and Silverman B. 1994. Nonparametric Regression and Generalized Linear Models. London, Chapman and Hall.
Hansen E. 1979. Global optimization using interval analysis: The onedimensional case. Journal of Optimization Theory and Applications 29: 331–344.
Hastie T.J. and Tibshirani R.J. 1990. Generalized Additive Models. London, Chapman and Hall. Monographs on Statistics and Applied Probability, Vol. 43.
Marron J.S. 1992. Discussion of “The performance of six popular bandwith selectors on some real datasets” by Sheather. Computational Statistics 7: 271–273.
Ratschek H. and Rokne J. 1988. New Computer Methods for Computer Optimization. Chichester, Ellis Horwood.
Thompson A.M., Brown J.C., Kay J.W., and Titterington D.M. 1991. A study of methods of choosing the smoothing parameter in image restoration by regularization. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-13: 326–339.
Thompson A., Kay J., and TitteringtonD. 1989. A cautionary note about cross-validatory choice. J. Statist. Comput. Simul. 33: 199–216.
Tikhonov A.N. and Arsenin V.Y. 1977. Solutions of Ill-Posed Problems. Washington, DC, Winston.
Törn A. and Žilinskas A. 1989. Global Optimization. Berlin, Springer-Verlag. Lecture Notes in Computer Science, Vol. 350.
Wahba G. 1990. Spline Models for Observational Data. Philadelphia, Society for Industrial and Applied Mathematics.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kent, J.T., Mohammadzadeh, M. Global optimization of the generalized cross-validation criterion. Statistics and Computing 10, 231–236 (2000). https://doi.org/10.1023/A:1008939510946
Issue Date:
DOI: https://doi.org/10.1023/A:1008939510946