# Smoothing Parameter Selection Using Multifold Cross-Validation in Smoothing Spline Regressions

• Published : 1998.08.01

#### Abstract

The smoothing parameter $\lambda$ in smoothing spline regression is usually selected by minimizing cross-validation (CV) or generalized cross-validation (GCV). But, simple CV or GCV is poor candidate for estimating prediction error. We defined MGCV (Multifold Generalized Cross-validation) as a criterion for selecting smoothing parameter in smoothing spline regression. This is a version of cross-validation using $leave-\kappa-out$ method. Some numerical results comparing MGCV and GCV are done.

#### References

1. IEEE Transactions on Automatic Control v.19 A new look at statistical model identification Akaike, H.
2. Biometrika v.71 An alternative method of cross-validation for the smoothing of density estimates Bowman, A.W.
3. Biometrika v.76 A comparative study of ordinary cross-validation, u-fold cross-validation and the repeated learning-testing methods Burman, P.
4. Journal of SIAM v.21 Multivariate smoothing spline functions Cox, D. D.
5. Numerische Mathematik v.31 Smoothing noisy data with spline function : Estimating the correct degree of smoothing by the method of generalized cross-validation Craven, P.;Wahba, G.
6. Journal of the American Statistical Association v.78 Estimating the error rate of a prediction rule: Improvement on cross-validation Efron, B.
7. Journal of the American Statistical Association v.81 How biased is the apparent error rate of a prediction rule? Efron, B.
8. Spline Smoothing and Nonparametric Regression Eubank, R.L.
9. Journal of the American Statistical Association v.70 The predictive sample reuse method with application Geisser, S.
10. The Annals of Statistics v.13 Optimal bandwidth selection in nonparametric regression function estimation Hardle, W.;Marron, J. S.
11. Ph. D. Thesis, Department of Statistics Pusan National University A Study on model checking in nonparametric regression Jeong, M.
12. Statistics and Probability Letters v.31 Cook's distance in spline smoothing Kim, C.
13. The Annals of Statistics v.14 Asymptotic optimality of $C_L$ and generalized cross-validation in ridge regression with application to spline smoothing Li, K. C.
14. Some comment on $C_p$, {＼em Technometrics} v.15 Mallows, C.L.
15. Journal of the American Statistical Association v.88 Linear model selection by cross-validation Shao, J.
16. Biometrika v.68 On optimal selection of regression variables Shibata, R.
17. Journal of the Royal Statistical Society, ser. B. v.47 Some aspects of the spline smoothing approach to nonparametric regression curve fitting (with discussion) Silverman, B.W.
18. Efficient nonparametric regression with cross-validated smoothing splines Speckman, P.
19. Journal of the Royal Statistical Society, ser. B. v.36 Cross-validatory choice and assessment of statistical prediction (with discussion) Stone, M.
20. Journal of SIAM v.14 Practical approximate solutions to linear operator equations when the data are noisy Wahba, G.
21. Spline Models for Observational Data Wahba, G.
22. Journal of the American Statistical Association v.78 Splines in statistics Wegman, E.J.;Wright, I.W.
23. The Annals of Statistics v.21 Model selection via multifold cross-validation Zhang, P.