You are here

Smoothing Parameter Selection for Nonparametric Regression Using Smoothing Spline

Journal Name:

Publication Year:

Abstract (2. Language): 
In this paper, the smoothing parameter selection problem has been examined in respect to a smoothing spline implementation in predicting nonparametric regression models. For this purpose, a simulation study has been performed by using a program written in MATLAB. The simulation study provides a comparison of the nine smoothing parameter selection methods. In this connection, 500 replications have been performed in simulation for sample sets with different sizes. Thus, the appropriate selection criteria are provided for a suitable smoothing parameter selection.



[13] T Krivobokova, C M Crainiceanu, and G Kauermann. Fast adaptive penalized splines.
Journal of Computational and Graphical Statistics, 17:1–20, 2008.
[14] T Krivobokova and G Kauermann. A note on penalized spline smoothing with correlated
errors. Journal of the American Statistical Association, 102:1328–337, 2007.
[15] T C M Lee. Smoothing parameter selection for smoothing splines: A simulation study.
Computational Statistics & Data Analysis, 42:139–148, 2003.
[16] T C M Lee. Improved smoothing spline regression by combining estimates of different
smoothness. Statistics & Probability Letters, 67:133–140, 2004.
[17] T C M Lee and V Solo. Bandwidth selection for local linear regression: A simulation
study. Computational Statistics & Data Analysis, 14:515–532, 1999.
[18] C Mallows’. Some comments on cp. Technometrics, 15:661–375, 1973.
[19] J Rice. Bandwidth choice for nonparametric regression. Annals of Statistics, 12:1215–
1230, 1984.
[20] T Robinson and R Moyeed. Making robust the cross-validation choice of smoothing parameter
in spline regression. Communications in Statistics - Theory and Methods, 18:523–
539, 1989.
[21] D Ruppert, M PWand, and R J Carroll. Semiparametric Regression. Cambridge University
Press, Cambridge, 2003.
[22] G M Schimek. Smoothing and Regression: Approaches, Computation, and Application.
John Willey & Sons, Inc., USA, 2000.
[23] R Shibata. An optimal selection of regression variables. Biometrika, 68(1):45–45, 1981.
[24] M Stone. An asymptotic equivalence of choice of model by cross-validation and akaike’s
criterion. Journal of the Royal Statistical Society. Series B (Statistical Methodology),
39:44–47, 1977.
[25] G Wahba. A comparison of gcv and gml for choosing the smoothing parameter in the
generalized spline smoothing problem. Annals of Statistics, 13:1378–1402, 1985.
[26] G Wahba. Spline Model For Observational Data. Siam, Philadelphia, 1990.
[27] C Yanrong, Z W Tracy L Haiqun, and Y Yan. Penalized spline estimation for functional
coefficient regression models. Computational Statistics and Data Analysis, 54:891–905,

Thank you for copying data from