A Comparison of the Nonparametric Regression Models using Smoothing Spline and Kernel Regression

Authors: Dursun Aydin

Abstract:

This paper study about using of nonparametric models for Gross National Product data in Turkey and Stanford heart transplant data. It is discussed two nonparametric techniques called smoothing spline and kernel regression. The main goal is to compare the techniques used for prediction of the nonparametric regression models. According to the results of numerical studies, it is concluded that smoothing spline regression estimators are better than those of the kernel regression.

Keywords: Kernel regression, Nonparametric models, Prediction, Smoothing spline.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1332448

References:

[1] Hastie, T.J. and Tibshirani, R.J., Generalized Additive Models, Chapman & Hall /CRC, 1999.
[2] Wahba, G., Spline Model For Observational Data, Siam, Philadelphia Pa., 1990.
[3] Green, P. J. and Silverman, B. W., Nonparametric Regression and Generalized Linear Models, Chapman & Hall, 1994.
[4] Eubank, R. L., Nonparametric Regression and Smoothing Spline, Marcel Dekker Inc., 1999.
[5] Nadarya, E.A., On Estimating Regression, Theory Pb. Appl., Vol.10, 1964, pp. 186-190.
[6] Watson, G. S., Smooth Regression Analysis, Sankhya, Series A, Vol.26, 1964, pp.359-372.
[7] Yatchew, A., Semiparametric Regression for the Applied Econometrician, Cambridge University Pres, 2003.
[8] Wand, M,. P. Ve M. C. Jones, Kernel Smoothing, New York: Chapman and Hall, 1995.
[9] Hardle, W., Applied Nonparametric Regression, Cambridge University Press, Cambridge ,1991.
[10] Schimek, M. G., Smoothing and Regression, Jhon. Willy. & Sons, 2000.
[11] John Crowley, Marie Hu, Covariance Analysis of Heart Transplant Survival Data, Journal of the American Statistical Association, Vol. 72, No. 357 Mar., 1977, pp. 27-36.